id int64 1 14M | domain stringclasses 6
values | topic stringclasses 23
values | subtopic stringclasses 37
values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
values |
|---|---|---|---|---|---|---|---|---|---|---|
101 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.16 m/s, a=7.692 m/s²) | An object starts with initial velocity 27.16 m/s and experiences constant acceleration 7.692 m/s² for 2.754 s. Final velocity: v = v0 + a t = 27.16 + (7.692)(2.754) = 48.34 m/s. Displacement: s = v0 t + (1/2) a t² = 104 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
102 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.71 m/s, a=-0.8498 m/s²) | An object starts with initial velocity 12.71 m/s and experiences constant acceleration -0.8498 m/s² for 1.067 s. Final velocity: v = v0 + a t = 12.71 + (-0.8498)(1.067) = 11.8 m/s. Displacement: s = v0 t + (1/2) a t² = 13.08 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
103 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.13 m/s, a=4.557 m/s²) | An object starts with initial velocity 23.13 m/s and experiences constant acceleration 4.557 m/s² for 5.977 s. Final velocity: v = v0 + a t = 23.13 + (4.557)(5.977) = 50.37 m/s. Displacement: s = v0 t + (1/2) a t² = 219.7 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
104 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.24 m/s, a=3.275 m/s²) | An object starts with initial velocity 22.24 m/s and experiences constant acceleration 3.275 m/s² for 9.126 s. Final velocity: v = v0 + a t = 22.24 + (3.275)(9.126) = 52.13 m/s. Displacement: s = v0 t + (1/2) a t² = 339.3 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
105 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.2901 m/s, a=-3.871 m/s²) | An object starts with initial velocity 0.2901 m/s and experiences constant acceleration -3.871 m/s² for 17.78 s. Final velocity: v = v0 + a t = 0.2901 + (-3.871)(17.78) = -68.54 m/s. Displacement: s = v0 t + (1/2) a t² = -606.7 m. These relations follow directly from the definitions of average velocity and constant acc... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
106 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.12 m/s, a=3.184 m/s²) | An object starts with initial velocity 27.12 m/s and experiences constant acceleration 3.184 m/s² for 16.86 s. Final velocity: v = v0 + a t = 27.12 + (3.184)(16.86) = 80.79 m/s. Displacement: s = v0 t + (1/2) a t² = 909.5 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
107 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=17.48 m/s, a=-2.779 m/s²) | An object starts with initial velocity 17.48 m/s and experiences constant acceleration -2.779 m/s² for 3.421 s. Final velocity: v = v0 + a t = 17.48 + (-2.779)(3.421) = 7.968 m/s. Displacement: s = v0 t + (1/2) a t² = 43.53 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
108 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.248 m/s, a=8.485 m/s²) | An object starts with initial velocity 9.248 m/s and experiences constant acceleration 8.485 m/s² for 16.13 s. Final velocity: v = v0 + a t = 9.248 + (8.485)(16.13) = 146.1 m/s. Displacement: s = v0 t + (1/2) a t² = 1252 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
109 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.82 m/s, a=8.484 m/s²) | An object starts with initial velocity 25.82 m/s and experiences constant acceleration 8.484 m/s² for 4.991 s. Final velocity: v = v0 + a t = 25.82 + (8.484)(4.991) = 68.17 m/s. Displacement: s = v0 t + (1/2) a t² = 234.6 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
110 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.486 m/s, a=-3.458 m/s²) | An object starts with initial velocity 7.486 m/s and experiences constant acceleration -3.458 m/s² for 15.82 s. Final velocity: v = v0 + a t = 7.486 + (-3.458)(15.82) = -47.23 m/s. Displacement: s = v0 t + (1/2) a t² = -314.4 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
111 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.52 m/s, a=1.096 m/s²) | An object starts with initial velocity 26.52 m/s and experiences constant acceleration 1.096 m/s² for 12.79 s. Final velocity: v = v0 + a t = 26.52 + (1.096)(12.79) = 40.54 m/s. Displacement: s = v0 t + (1/2) a t² = 429 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
112 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.637 m/s, a=8.948 m/s²) | An object starts with initial velocity 4.637 m/s and experiences constant acceleration 8.948 m/s² for 17.43 s. Final velocity: v = v0 + a t = 4.637 + (8.948)(17.43) = 160.6 m/s. Displacement: s = v0 t + (1/2) a t² = 1440 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
113 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.29 m/s, a=7.162 m/s²) | An object starts with initial velocity 29.29 m/s and experiences constant acceleration 7.162 m/s² for 17.75 s. Final velocity: v = v0 + a t = 29.29 + (7.162)(17.75) = 156.4 m/s. Displacement: s = v0 t + (1/2) a t² = 1648 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
114 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.7436 m/s, a=6.048 m/s²) | An object starts with initial velocity 0.7436 m/s and experiences constant acceleration 6.048 m/s² for 7.312 s. Final velocity: v = v0 + a t = 0.7436 + (6.048)(7.312) = 44.97 m/s. Displacement: s = v0 t + (1/2) a t² = 167.1 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
115 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.92 m/s, a=7.034 m/s²) | An object starts with initial velocity 27.92 m/s and experiences constant acceleration 7.034 m/s² for 17.42 s. Final velocity: v = v0 + a t = 27.92 + (7.034)(17.42) = 150.4 m/s. Displacement: s = v0 t + (1/2) a t² = 1553 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
116 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.32 m/s, a=-0.9979 m/s²) | An object starts with initial velocity 24.32 m/s and experiences constant acceleration -0.9979 m/s² for 15.96 s. Final velocity: v = v0 + a t = 24.32 + (-0.9979)(15.96) = 8.396 m/s. Displacement: s = v0 t + (1/2) a t² = 261.1 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
117 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.243 m/s, a=8.083 m/s²) | An object starts with initial velocity 3.243 m/s and experiences constant acceleration 8.083 m/s² for 17.31 s. Final velocity: v = v0 + a t = 3.243 + (8.083)(17.31) = 143.2 m/s. Displacement: s = v0 t + (1/2) a t² = 1268 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
118 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.673 m/s, a=7.249 m/s²) | An object starts with initial velocity 6.673 m/s and experiences constant acceleration 7.249 m/s² for 9.746 s. Final velocity: v = v0 + a t = 6.673 + (7.249)(9.746) = 77.32 m/s. Displacement: s = v0 t + (1/2) a t² = 409.3 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
119 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.156 m/s, a=6.93 m/s²) | An object starts with initial velocity 9.156 m/s and experiences constant acceleration 6.93 m/s² for 5.324 s. Final velocity: v = v0 + a t = 9.156 + (6.93)(5.324) = 46.05 m/s. Displacement: s = v0 t + (1/2) a t² = 147 m. These relations follow directly from the definitions of average velocity and constant acceleration. | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
120 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.7099 m/s, a=-2.103 m/s²) | An object starts with initial velocity 0.7099 m/s and experiences constant acceleration -2.103 m/s² for 7.237 s. Final velocity: v = v0 + a t = 0.7099 + (-2.103)(7.237) = -14.51 m/s. Displacement: s = v0 t + (1/2) a t² = -49.93 m. These relations follow directly from the definitions of average velocity and constant acc... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
121 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.93 m/s, a=9.503 m/s²) | An object starts with initial velocity 25.93 m/s and experiences constant acceleration 9.503 m/s² for 6.303 s. Final velocity: v = v0 + a t = 25.93 + (9.503)(6.303) = 85.83 m/s. Displacement: s = v0 t + (1/2) a t² = 352.2 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
122 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.24 m/s, a=0.9952 m/s²) | An object starts with initial velocity 19.24 m/s and experiences constant acceleration 0.9952 m/s² for 19.64 s. Final velocity: v = v0 + a t = 19.24 + (0.9952)(19.64) = 38.79 m/s. Displacement: s = v0 t + (1/2) a t² = 570 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
123 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.09 m/s, a=9.089 m/s²) | An object starts with initial velocity 16.09 m/s and experiences constant acceleration 9.089 m/s² for 3.191 s. Final velocity: v = v0 + a t = 16.09 + (9.089)(3.191) = 45.09 m/s. Displacement: s = v0 t + (1/2) a t² = 97.63 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
124 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.11 m/s, a=-2.321 m/s²) | An object starts with initial velocity 29.11 m/s and experiences constant acceleration -2.321 m/s² for 19.29 s. Final velocity: v = v0 + a t = 29.11 + (-2.321)(19.29) = -15.67 m/s. Displacement: s = v0 t + (1/2) a t² = 129.7 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
125 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.964 m/s, a=-3.374 m/s²) | An object starts with initial velocity 7.964 m/s and experiences constant acceleration -3.374 m/s² for 9.257 s. Final velocity: v = v0 + a t = 7.964 + (-3.374)(9.257) = -23.27 m/s. Displacement: s = v0 t + (1/2) a t² = -70.83 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
126 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.86 m/s, a=-0.2948 m/s²) | An object starts with initial velocity 21.86 m/s and experiences constant acceleration -0.2948 m/s² for 12.52 s. Final velocity: v = v0 + a t = 21.86 + (-0.2948)(12.52) = 18.17 m/s. Displacement: s = v0 t + (1/2) a t² = 250.5 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
127 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.34 m/s, a=0.7779 m/s²) | An object starts with initial velocity 15.34 m/s and experiences constant acceleration 0.7779 m/s² for 11.96 s. Final velocity: v = v0 + a t = 15.34 + (0.7779)(11.96) = 24.64 m/s. Displacement: s = v0 t + (1/2) a t² = 239 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
128 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.642 m/s, a=5.632 m/s²) | An object starts with initial velocity 7.642 m/s and experiences constant acceleration 5.632 m/s² for 1.032 s. Final velocity: v = v0 + a t = 7.642 + (5.632)(1.032) = 13.45 m/s. Displacement: s = v0 t + (1/2) a t² = 10.89 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
129 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.77 m/s, a=3.077 m/s²) | An object starts with initial velocity 27.77 m/s and experiences constant acceleration 3.077 m/s² for 14.67 s. Final velocity: v = v0 + a t = 27.77 + (3.077)(14.67) = 72.9 m/s. Displacement: s = v0 t + (1/2) a t² = 738.4 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
130 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.26 m/s, a=5.059 m/s²) | An object starts with initial velocity 22.26 m/s and experiences constant acceleration 5.059 m/s² for 7.92 s. Final velocity: v = v0 + a t = 22.26 + (5.059)(7.92) = 62.33 m/s. Displacement: s = v0 t + (1/2) a t² = 335 m. These relations follow directly from the definitions of average velocity and constant acceleration. | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
131 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.099 m/s, a=4.964 m/s²) | An object starts with initial velocity 2.099 m/s and experiences constant acceleration 4.964 m/s² for 7.274 s. Final velocity: v = v0 + a t = 2.099 + (4.964)(7.274) = 38.2 m/s. Displacement: s = v0 t + (1/2) a t² = 146.6 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
132 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.417 m/s, a=7.72 m/s²) | An object starts with initial velocity 9.417 m/s and experiences constant acceleration 7.72 m/s² for 14.68 s. Final velocity: v = v0 + a t = 9.417 + (7.72)(14.68) = 122.7 m/s. Displacement: s = v0 t + (1/2) a t² = 969.5 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
133 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.01 m/s, a=-0.3607 m/s²) | An object starts with initial velocity 9.01 m/s and experiences constant acceleration -0.3607 m/s² for 8.759 s. Final velocity: v = v0 + a t = 9.01 + (-0.3607)(8.759) = 5.85 m/s. Displacement: s = v0 t + (1/2) a t² = 65.08 m. These relations follow directly from the definitions of average velocity and constant accelera... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
134 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.07 m/s, a=-0.5652 m/s²) | An object starts with initial velocity 12.07 m/s and experiences constant acceleration -0.5652 m/s² for 3.418 s. Final velocity: v = v0 + a t = 12.07 + (-0.5652)(3.418) = 10.14 m/s. Displacement: s = v0 t + (1/2) a t² = 37.97 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
135 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.61 m/s, a=9.105 m/s²) | An object starts with initial velocity 12.61 m/s and experiences constant acceleration 9.105 m/s² for 13.87 s. Final velocity: v = v0 + a t = 12.61 + (9.105)(13.87) = 138.9 m/s. Displacement: s = v0 t + (1/2) a t² = 1051 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
136 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.08 m/s, a=4.233 m/s²) | An object starts with initial velocity 27.08 m/s and experiences constant acceleration 4.233 m/s² for 6.718 s. Final velocity: v = v0 + a t = 27.08 + (4.233)(6.718) = 55.52 m/s. Displacement: s = v0 t + (1/2) a t² = 277.5 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
137 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.44 m/s, a=-4.994 m/s²) | An object starts with initial velocity 16.44 m/s and experiences constant acceleration -4.994 m/s² for 6.451 s. Final velocity: v = v0 + a t = 16.44 + (-4.994)(6.451) = -15.78 m/s. Displacement: s = v0 t + (1/2) a t² = 2.125 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
138 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.9 m/s, a=3.7 m/s²) | An object starts with initial velocity 12.9 m/s and experiences constant acceleration 3.7 m/s² for 13.44 s. Final velocity: v = v0 + a t = 12.9 + (3.7)(13.44) = 62.62 m/s. Displacement: s = v0 t + (1/2) a t² = 507.4 m. These relations follow directly from the definitions of average velocity and constant acceleration. | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
139 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.95 m/s, a=1.632 m/s²) | An object starts with initial velocity 13.95 m/s and experiences constant acceleration 1.632 m/s² for 5.06 s. Final velocity: v = v0 + a t = 13.95 + (1.632)(5.06) = 22.21 m/s. Displacement: s = v0 t + (1/2) a t² = 91.49 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
140 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.2 m/s, a=8.518 m/s²) | An object starts with initial velocity 14.2 m/s and experiences constant acceleration 8.518 m/s² for 16.12 s. Final velocity: v = v0 + a t = 14.2 + (8.518)(16.12) = 151.5 m/s. Displacement: s = v0 t + (1/2) a t² = 1336 m. These relations follow directly from the definitions of average velocity and constant acceleration... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
141 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.091 m/s, a=-3.728 m/s²) | An object starts with initial velocity 5.091 m/s and experiences constant acceleration -3.728 m/s² for 10.79 s. Final velocity: v = v0 + a t = 5.091 + (-3.728)(10.79) = -35.15 m/s. Displacement: s = v0 t + (1/2) a t² = -162.2 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
142 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.99 m/s, a=0.02782 m/s²) | An object starts with initial velocity 18.99 m/s and experiences constant acceleration 0.02782 m/s² for 16.55 s. Final velocity: v = v0 + a t = 18.99 + (0.02782)(16.55) = 19.45 m/s. Displacement: s = v0 t + (1/2) a t² = 318.1 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
143 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.53 m/s, a=5.092 m/s²) | An object starts with initial velocity 22.53 m/s and experiences constant acceleration 5.092 m/s² for 5.268 s. Final velocity: v = v0 + a t = 22.53 + (5.092)(5.268) = 49.36 m/s. Displacement: s = v0 t + (1/2) a t² = 189.4 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
144 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.974 m/s, a=-4.634 m/s²) | An object starts with initial velocity 5.974 m/s and experiences constant acceleration -4.634 m/s² for 5.652 s. Final velocity: v = v0 + a t = 5.974 + (-4.634)(5.652) = -20.22 m/s. Displacement: s = v0 t + (1/2) a t² = -40.25 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
145 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.25 m/s, a=7.746 m/s²) | An object starts with initial velocity 14.25 m/s and experiences constant acceleration 7.746 m/s² for 2.384 s. Final velocity: v = v0 + a t = 14.25 + (7.746)(2.384) = 32.72 m/s. Displacement: s = v0 t + (1/2) a t² = 55.99 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
146 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.43 m/s, a=4.446 m/s²) | An object starts with initial velocity 12.43 m/s and experiences constant acceleration 4.446 m/s² for 4.694 s. Final velocity: v = v0 + a t = 12.43 + (4.446)(4.694) = 33.31 m/s. Displacement: s = v0 t + (1/2) a t² = 107.4 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
147 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.89 m/s, a=2.416 m/s²) | An object starts with initial velocity 20.89 m/s and experiences constant acceleration 2.416 m/s² for 5.636 s. Final velocity: v = v0 + a t = 20.89 + (2.416)(5.636) = 34.5 m/s. Displacement: s = v0 t + (1/2) a t² = 156.1 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
148 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.68 m/s, a=-4.917 m/s²) | An object starts with initial velocity 19.68 m/s and experiences constant acceleration -4.917 m/s² for 15.27 s. Final velocity: v = v0 + a t = 19.68 + (-4.917)(15.27) = -55.39 m/s. Displacement: s = v0 t + (1/2) a t² = -272.6 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
149 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.1 m/s, a=-3.401 m/s²) | An object starts with initial velocity 23.1 m/s and experiences constant acceleration -3.401 m/s² for 9.078 s. Final velocity: v = v0 + a t = 23.1 + (-3.401)(9.078) = -7.774 m/s. Displacement: s = v0 t + (1/2) a t² = 69.57 m. These relations follow directly from the definitions of average velocity and constant accelera... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
150 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.277 m/s, a=9.369 m/s²) | An object starts with initial velocity 5.277 m/s and experiences constant acceleration 9.369 m/s² for 10.84 s. Final velocity: v = v0 + a t = 5.277 + (9.369)(10.84) = 106.9 m/s. Displacement: s = v0 t + (1/2) a t² = 607.8 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
151 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.507 m/s, a=-1.262 m/s²) | An object starts with initial velocity 1.507 m/s and experiences constant acceleration -1.262 m/s² for 17.12 s. Final velocity: v = v0 + a t = 1.507 + (-1.262)(17.12) = -20.1 m/s. Displacement: s = v0 t + (1/2) a t² = -159.1 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
152 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.69 m/s, a=7.021 m/s²) | An object starts with initial velocity 13.69 m/s and experiences constant acceleration 7.021 m/s² for 13.68 s. Final velocity: v = v0 + a t = 13.69 + (7.021)(13.68) = 109.8 m/s. Displacement: s = v0 t + (1/2) a t² = 844.8 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
153 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.64 m/s, a=3.932 m/s²) | An object starts with initial velocity 29.64 m/s and experiences constant acceleration 3.932 m/s² for 19.05 s. Final velocity: v = v0 + a t = 29.64 + (3.932)(19.05) = 104.5 m/s. Displacement: s = v0 t + (1/2) a t² = 1278 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
154 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.74 m/s, a=4.19 m/s²) | An object starts with initial velocity 26.74 m/s and experiences constant acceleration 4.19 m/s² for 14.67 s. Final velocity: v = v0 + a t = 26.74 + (4.19)(14.67) = 88.19 m/s. Displacement: s = v0 t + (1/2) a t² = 842.8 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
155 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.14 m/s, a=7.459 m/s²) | An object starts with initial velocity 15.14 m/s and experiences constant acceleration 7.459 m/s² for 11.41 s. Final velocity: v = v0 + a t = 15.14 + (7.459)(11.41) = 100.2 m/s. Displacement: s = v0 t + (1/2) a t² = 658.2 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
156 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.92 m/s, a=6.155 m/s²) | An object starts with initial velocity 26.92 m/s and experiences constant acceleration 6.155 m/s² for 10.02 s. Final velocity: v = v0 + a t = 26.92 + (6.155)(10.02) = 88.58 m/s. Displacement: s = v0 t + (1/2) a t² = 578.6 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
157 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.776 m/s, a=-1.291 m/s²) | An object starts with initial velocity 7.776 m/s and experiences constant acceleration -1.291 m/s² for 13.12 s. Final velocity: v = v0 + a t = 7.776 + (-1.291)(13.12) = -9.162 m/s. Displacement: s = v0 t + (1/2) a t² = -9.089 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
158 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.97 m/s, a=2.819 m/s²) | An object starts with initial velocity 22.97 m/s and experiences constant acceleration 2.819 m/s² for 12.91 s. Final velocity: v = v0 + a t = 22.97 + (2.819)(12.91) = 59.37 m/s. Displacement: s = v0 t + (1/2) a t² = 531.5 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
159 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.238 m/s, a=-3.838 m/s²) | An object starts with initial velocity 8.238 m/s and experiences constant acceleration -3.838 m/s² for 6.429 s. Final velocity: v = v0 + a t = 8.238 + (-3.838)(6.429) = -16.43 m/s. Displacement: s = v0 t + (1/2) a t² = -26.35 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
160 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.151 m/s, a=-0.2044 m/s²) | An object starts with initial velocity 8.151 m/s and experiences constant acceleration -0.2044 m/s² for 11.26 s. Final velocity: v = v0 + a t = 8.151 + (-0.2044)(11.26) = 5.85 m/s. Displacement: s = v0 t + (1/2) a t² = 78.85 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
161 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.151 m/s, a=-1.531 m/s²) | An object starts with initial velocity 4.151 m/s and experiences constant acceleration -1.531 m/s² for 14.19 s. Final velocity: v = v0 + a t = 4.151 + (-1.531)(14.19) = -17.57 m/s. Displacement: s = v0 t + (1/2) a t² = -95.15 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
162 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.19 m/s, a=-4.037 m/s²) | An object starts with initial velocity 21.19 m/s and experiences constant acceleration -4.037 m/s² for 8.744 s. Final velocity: v = v0 + a t = 21.19 + (-4.037)(8.744) = -14.1 m/s. Displacement: s = v0 t + (1/2) a t² = 30.99 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
163 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.28 m/s, a=1.237 m/s²) | An object starts with initial velocity 16.28 m/s and experiences constant acceleration 1.237 m/s² for 4.93 s. Final velocity: v = v0 + a t = 16.28 + (1.237)(4.93) = 22.37 m/s. Displacement: s = v0 t + (1/2) a t² = 95.28 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
164 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.6 m/s, a=8.573 m/s²) | An object starts with initial velocity 12.6 m/s and experiences constant acceleration 8.573 m/s² for 12.1 s. Final velocity: v = v0 + a t = 12.6 + (8.573)(12.1) = 116.3 m/s. Displacement: s = v0 t + (1/2) a t² = 779.8 m. These relations follow directly from the definitions of average velocity and constant acceleration. | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
165 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.87 m/s, a=7.851 m/s²) | An object starts with initial velocity 20.87 m/s and experiences constant acceleration 7.851 m/s² for 15.55 s. Final velocity: v = v0 + a t = 20.87 + (7.851)(15.55) = 142.9 m/s. Displacement: s = v0 t + (1/2) a t² = 1273 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
166 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.41 m/s, a=-4.912 m/s²) | An object starts with initial velocity 11.41 m/s and experiences constant acceleration -4.912 m/s² for 7.683 s. Final velocity: v = v0 + a t = 11.41 + (-4.912)(7.683) = -26.33 m/s. Displacement: s = v0 t + (1/2) a t² = -57.3 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
167 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.6 m/s, a=7.802 m/s²) | An object starts with initial velocity 22.6 m/s and experiences constant acceleration 7.802 m/s² for 19.12 s. Final velocity: v = v0 + a t = 22.6 + (7.802)(19.12) = 171.7 m/s. Displacement: s = v0 t + (1/2) a t² = 1857 m. These relations follow directly from the definitions of average velocity and constant acceleration... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
168 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.57 m/s, a=6.213 m/s²) | An object starts with initial velocity 12.57 m/s and experiences constant acceleration 6.213 m/s² for 11.38 s. Final velocity: v = v0 + a t = 12.57 + (6.213)(11.38) = 83.25 m/s. Displacement: s = v0 t + (1/2) a t² = 545.1 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
169 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.1 m/s, a=-1.692 m/s²) | An object starts with initial velocity 18.1 m/s and experiences constant acceleration -1.692 m/s² for 5.169 s. Final velocity: v = v0 + a t = 18.1 + (-1.692)(5.169) = 9.352 m/s. Displacement: s = v0 t + (1/2) a t² = 70.94 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
170 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.08 m/s, a=-4.565 m/s²) | An object starts with initial velocity 13.08 m/s and experiences constant acceleration -4.565 m/s² for 7.386 s. Final velocity: v = v0 + a t = 13.08 + (-4.565)(7.386) = -20.64 m/s. Displacement: s = v0 t + (1/2) a t² = -27.94 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
171 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.37 m/s, a=1.065 m/s²) | An object starts with initial velocity 20.37 m/s and experiences constant acceleration 1.065 m/s² for 4.136 s. Final velocity: v = v0 + a t = 20.37 + (1.065)(4.136) = 24.78 m/s. Displacement: s = v0 t + (1/2) a t² = 93.37 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
172 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.02 m/s, a=-3.086 m/s²) | An object starts with initial velocity 14.02 m/s and experiences constant acceleration -3.086 m/s² for 12.82 s. Final velocity: v = v0 + a t = 14.02 + (-3.086)(12.82) = -25.54 m/s. Displacement: s = v0 t + (1/2) a t² = -73.88 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
173 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.809 m/s, a=0.9103 m/s²) | An object starts with initial velocity 0.809 m/s and experiences constant acceleration 0.9103 m/s² for 11.72 s. Final velocity: v = v0 + a t = 0.809 + (0.9103)(11.72) = 11.48 m/s. Displacement: s = v0 t + (1/2) a t² = 72.04 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
174 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.8131 m/s, a=4.641 m/s²) | An object starts with initial velocity 0.8131 m/s and experiences constant acceleration 4.641 m/s² for 3.578 s. Final velocity: v = v0 + a t = 0.8131 + (4.641)(3.578) = 17.42 m/s. Displacement: s = v0 t + (1/2) a t² = 32.62 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
175 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.85 m/s, a=-4.246 m/s²) | An object starts with initial velocity 13.85 m/s and experiences constant acceleration -4.246 m/s² for 8.203 s. Final velocity: v = v0 + a t = 13.85 + (-4.246)(8.203) = -20.98 m/s. Displacement: s = v0 t + (1/2) a t² = -29.23 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
176 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.35 m/s, a=-0.09731 m/s²) | An object starts with initial velocity 6.35 m/s and experiences constant acceleration -0.09731 m/s² for 15.46 s. Final velocity: v = v0 + a t = 6.35 + (-0.09731)(15.46) = 4.845 m/s. Displacement: s = v0 t + (1/2) a t² = 86.55 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
177 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.37 m/s, a=6.28 m/s²) | An object starts with initial velocity 11.37 m/s and experiences constant acceleration 6.28 m/s² for 16.81 s. Final velocity: v = v0 + a t = 11.37 + (6.28)(16.81) = 116.9 m/s. Displacement: s = v0 t + (1/2) a t² = 1078 m. These relations follow directly from the definitions of average velocity and constant acceleration... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
178 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.568 m/s, a=-3.771 m/s²) | An object starts with initial velocity 7.568 m/s and experiences constant acceleration -3.771 m/s² for 1.368 s. Final velocity: v = v0 + a t = 7.568 + (-3.771)(1.368) = 2.408 m/s. Displacement: s = v0 t + (1/2) a t² = 6.825 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
179 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.18 m/s, a=9.999 m/s²) | An object starts with initial velocity 16.18 m/s and experiences constant acceleration 9.999 m/s² for 7.649 s. Final velocity: v = v0 + a t = 16.18 + (9.999)(7.649) = 92.66 m/s. Displacement: s = v0 t + (1/2) a t² = 416.3 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
180 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.5 m/s, a=6.718 m/s²) | An object starts with initial velocity 19.5 m/s and experiences constant acceleration 6.718 m/s² for 13.38 s. Final velocity: v = v0 + a t = 19.5 + (6.718)(13.38) = 109.4 m/s. Displacement: s = v0 t + (1/2) a t² = 862.7 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
181 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.63 m/s, a=9.244 m/s²) | An object starts with initial velocity 22.63 m/s and experiences constant acceleration 9.244 m/s² for 4.788 s. Final velocity: v = v0 + a t = 22.63 + (9.244)(4.788) = 66.89 m/s. Displacement: s = v0 t + (1/2) a t² = 214.3 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
182 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.6114 m/s, a=-2.714 m/s²) | An object starts with initial velocity 0.6114 m/s and experiences constant acceleration -2.714 m/s² for 3.398 s. Final velocity: v = v0 + a t = 0.6114 + (-2.714)(3.398) = -8.612 m/s. Displacement: s = v0 t + (1/2) a t² = -13.59 m. These relations follow directly from the definitions of average velocity and constant acc... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
183 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.08 m/s, a=3.46 m/s²) | An object starts with initial velocity 20.08 m/s and experiences constant acceleration 3.46 m/s² for 5.141 s. Final velocity: v = v0 + a t = 20.08 + (3.46)(5.141) = 37.87 m/s. Displacement: s = v0 t + (1/2) a t² = 149 m. These relations follow directly from the definitions of average velocity and constant acceleration. | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
184 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.98 m/s, a=6.503 m/s²) | An object starts with initial velocity 20.98 m/s and experiences constant acceleration 6.503 m/s² for 4.188 s. Final velocity: v = v0 + a t = 20.98 + (6.503)(4.188) = 48.22 m/s. Displacement: s = v0 t + (1/2) a t² = 144.9 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
185 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.22 m/s, a=6.219 m/s²) | An object starts with initial velocity 18.22 m/s and experiences constant acceleration 6.219 m/s² for 3.176 s. Final velocity: v = v0 + a t = 18.22 + (6.219)(3.176) = 37.97 m/s. Displacement: s = v0 t + (1/2) a t² = 89.23 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
186 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.58 m/s, a=9.471 m/s²) | An object starts with initial velocity 24.58 m/s and experiences constant acceleration 9.471 m/s² for 3.054 s. Final velocity: v = v0 + a t = 24.58 + (9.471)(3.054) = 53.5 m/s. Displacement: s = v0 t + (1/2) a t² = 119.2 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
187 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.7704 m/s, a=-0.3206 m/s²) | An object starts with initial velocity 0.7704 m/s and experiences constant acceleration -0.3206 m/s² for 13.87 s. Final velocity: v = v0 + a t = 0.7704 + (-0.3206)(13.87) = -3.677 m/s. Displacement: s = v0 t + (1/2) a t² = -20.16 m. These relations follow directly from the definitions of average velocity and constant a... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
188 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.75 m/s, a=0.9498 m/s²) | An object starts with initial velocity 28.75 m/s and experiences constant acceleration 0.9498 m/s² for 14.59 s. Final velocity: v = v0 + a t = 28.75 + (0.9498)(14.59) = 42.6 m/s. Displacement: s = v0 t + (1/2) a t² = 520.3 m. These relations follow directly from the definitions of average velocity and constant accelera... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
189 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.28 m/s, a=5.359 m/s²) | An object starts with initial velocity 2.28 m/s and experiences constant acceleration 5.359 m/s² for 12.92 s. Final velocity: v = v0 + a t = 2.28 + (5.359)(12.92) = 71.51 m/s. Displacement: s = v0 t + (1/2) a t² = 476.6 m. These relations follow directly from the definitions of average velocity and constant acceleratio... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
190 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.057 m/s, a=6.587 m/s²) | An object starts with initial velocity 3.057 m/s and experiences constant acceleration 6.587 m/s² for 17.16 s. Final velocity: v = v0 + a t = 3.057 + (6.587)(17.16) = 116.1 m/s. Displacement: s = v0 t + (1/2) a t² = 1022 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
191 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.01 m/s, a=-3.184 m/s²) | An object starts with initial velocity 18.01 m/s and experiences constant acceleration -3.184 m/s² for 19.69 s. Final velocity: v = v0 + a t = 18.01 + (-3.184)(19.69) = -44.69 m/s. Displacement: s = v0 t + (1/2) a t² = -262.7 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
192 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.48 m/s, a=0.2081 m/s²) | An object starts with initial velocity 23.48 m/s and experiences constant acceleration 0.2081 m/s² for 9.139 s. Final velocity: v = v0 + a t = 23.48 + (0.2081)(9.139) = 25.38 m/s. Displacement: s = v0 t + (1/2) a t² = 223.3 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
193 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.12 m/s, a=2.589 m/s²) | An object starts with initial velocity 11.12 m/s and experiences constant acceleration 2.589 m/s² for 7.483 s. Final velocity: v = v0 + a t = 11.12 + (2.589)(7.483) = 30.49 m/s. Displacement: s = v0 t + (1/2) a t² = 155.7 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
194 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.49 m/s, a=7.335 m/s²) | An object starts with initial velocity 25.49 m/s and experiences constant acceleration 7.335 m/s² for 3.005 s. Final velocity: v = v0 + a t = 25.49 + (7.335)(3.005) = 47.53 m/s. Displacement: s = v0 t + (1/2) a t² = 109.7 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
195 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.82 m/s, a=4.534 m/s²) | An object starts with initial velocity 28.82 m/s and experiences constant acceleration 4.534 m/s² for 16.75 s. Final velocity: v = v0 + a t = 28.82 + (4.534)(16.75) = 104.7 m/s. Displacement: s = v0 t + (1/2) a t² = 1118 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
196 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.22 m/s, a=1.532 m/s²) | An object starts with initial velocity 21.22 m/s and experiences constant acceleration 1.532 m/s² for 14.94 s. Final velocity: v = v0 + a t = 21.22 + (1.532)(14.94) = 44.12 m/s. Displacement: s = v0 t + (1/2) a t² = 488.1 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
197 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.96 m/s, a=-0.9488 m/s²) | An object starts with initial velocity 28.96 m/s and experiences constant acceleration -0.9488 m/s² for 16.36 s. Final velocity: v = v0 + a t = 28.96 + (-0.9488)(16.36) = 13.45 m/s. Displacement: s = v0 t + (1/2) a t² = 346.8 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
198 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.15 m/s, a=2.252 m/s²) | An object starts with initial velocity 16.15 m/s and experiences constant acceleration 2.252 m/s² for 9.276 s. Final velocity: v = v0 + a t = 16.15 + (2.252)(9.276) = 37.04 m/s. Displacement: s = v0 t + (1/2) a t² = 246.7 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
199 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.93 m/s, a=-0.9741 m/s²) | An object starts with initial velocity 21.93 m/s and experiences constant acceleration -0.9741 m/s² for 17.18 s. Final velocity: v = v0 + a t = 21.93 + (-0.9741)(17.18) = 5.194 m/s. Displacement: s = v0 t + (1/2) a t² = 233 m. These relations follow directly from the definitions of average velocity and constant acceler... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
200 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.92 m/s, a=-3.7 m/s²) | An object starts with initial velocity 24.92 m/s and experiences constant acceleration -3.7 m/s² for 17.75 s. Final velocity: v = v0 + a t = 24.92 + (-3.7)(17.75) = -40.76 m/s. Displacement: s = v0 t + (1/2) a t² = -140.6 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.