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values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
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5,301 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.255 m/s, a=-3.209 m/s²) | An object starts with initial velocity 3.255 m/s and experiences constant acceleration -3.209 m/s² for 16.63 s. Final velocity: v = v0 + a t = 3.255 + (-3.209)(16.63) = -50.13 m/s. Displacement: s = v0 t + (1/2) a t² = -389.8 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. |
5,302 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.52 m/s, a=9.253 m/s²) | An object starts with initial velocity 26.52 m/s and experiences constant acceleration 9.253 m/s² for 11.54 s. Final velocity: v = v0 + a t = 26.52 + (9.253)(11.54) = 133.3 m/s. Displacement: s = v0 t + (1/2) a t² = 922.2 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. |
5,303 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.94 m/s, a=-3.093 m/s²) | An object starts with initial velocity 14.94 m/s and experiences constant acceleration -3.093 m/s² for 19.92 s. Final velocity: v = v0 + a t = 14.94 + (-3.093)(19.92) = -46.67 m/s. Displacement: s = v0 t + (1/2) a t² = -315.9 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. |
5,304 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.07 m/s, a=-3.36 m/s²) | An object starts with initial velocity 14.07 m/s and experiences constant acceleration -3.36 m/s² for 5.344 s. Final velocity: v = v0 + a t = 14.07 + (-3.36)(5.344) = -3.887 m/s. Displacement: s = v0 t + (1/2) a t² = 27.21 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. |
5,305 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.99 m/s, a=-2.233 m/s²) | An object starts with initial velocity 24.99 m/s and experiences constant acceleration -2.233 m/s² for 15.49 s. Final velocity: v = v0 + a t = 24.99 + (-2.233)(15.49) = -9.59 m/s. Displacement: s = v0 t + (1/2) a t² = 119.3 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. |
5,306 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.19 m/s, a=-1.374 m/s²) | An object starts with initial velocity 24.19 m/s and experiences constant acceleration -1.374 m/s² for 12.69 s. Final velocity: v = v0 + a t = 24.19 + (-1.374)(12.69) = 6.758 m/s. Displacement: s = v0 t + (1/2) a t² = 196.4 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. |
5,307 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.14 m/s, a=-2.859 m/s²) | An object starts with initial velocity 13.14 m/s and experiences constant acceleration -2.859 m/s² for 12.34 s. Final velocity: v = v0 + a t = 13.14 + (-2.859)(12.34) = -22.14 m/s. Displacement: s = v0 t + (1/2) a t² = -55.53 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. |
5,308 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.232 m/s, a=9.004 m/s²) | An object starts with initial velocity 1.232 m/s and experiences constant acceleration 9.004 m/s² for 15.57 s. Final velocity: v = v0 + a t = 1.232 + (9.004)(15.57) = 141.4 m/s. Displacement: s = v0 t + (1/2) a t² = 1110 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. |
5,309 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.669 m/s, a=-1.844 m/s²) | An object starts with initial velocity 5.669 m/s and experiences constant acceleration -1.844 m/s² for 7.041 s. Final velocity: v = v0 + a t = 5.669 + (-1.844)(7.041) = -7.31 m/s. Displacement: s = v0 t + (1/2) a t² = -5.777 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. |
5,310 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=17.06 m/s, a=9.229 m/s²) | An object starts with initial velocity 17.06 m/s and experiences constant acceleration 9.229 m/s² for 7.486 s. Final velocity: v = v0 + a t = 17.06 + (9.229)(7.486) = 86.15 m/s. Displacement: s = v0 t + (1/2) a t² = 386.3 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. |
5,311 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.51 m/s, a=8.828 m/s²) | An object starts with initial velocity 28.51 m/s and experiences constant acceleration 8.828 m/s² for 7.652 s. Final velocity: v = v0 + a t = 28.51 + (8.828)(7.652) = 96.06 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 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. |
5,312 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.019 m/s, a=4.662 m/s²) | An object starts with initial velocity 6.019 m/s and experiences constant acceleration 4.662 m/s² for 8.435 s. Final velocity: v = v0 + a t = 6.019 + (4.662)(8.435) = 45.34 m/s. Displacement: s = v0 t + (1/2) a t² = 216.6 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. |
5,313 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.593 m/s, a=-0.6229 m/s²) | An object starts with initial velocity 4.593 m/s and experiences constant acceleration -0.6229 m/s² for 2.209 s. Final velocity: v = v0 + a t = 4.593 + (-0.6229)(2.209) = 3.217 m/s. Displacement: s = v0 t + (1/2) a t² = 8.627 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. |
5,314 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.519 m/s, a=-2.085 m/s²) | An object starts with initial velocity 5.519 m/s and experiences constant acceleration -2.085 m/s² for 13.5 s. Final velocity: v = v0 + a t = 5.519 + (-2.085)(13.5) = -22.63 m/s. Displacement: s = v0 t + (1/2) a t² = -115.5 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. |
5,315 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.17 m/s, a=8.07 m/s²) | An object starts with initial velocity 13.17 m/s and experiences constant acceleration 8.07 m/s² for 2.318 s. Final velocity: v = v0 + a t = 13.17 + (8.07)(2.318) = 31.87 m/s. Displacement: s = v0 t + (1/2) a t² = 52.21 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. |
5,316 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.373 m/s, a=2.928 m/s²) | An object starts with initial velocity 7.373 m/s and experiences constant acceleration 2.928 m/s² for 11.58 s. Final velocity: v = v0 + a t = 7.373 + (2.928)(11.58) = 41.28 m/s. Displacement: s = v0 t + (1/2) a t² = 281.7 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. |
5,317 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.301 m/s, a=9.463 m/s²) | An object starts with initial velocity 4.301 m/s and experiences constant acceleration 9.463 m/s² for 2.078 s. Final velocity: v = v0 + a t = 4.301 + (9.463)(2.078) = 23.96 m/s. Displacement: s = v0 t + (1/2) a t² = 29.36 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. |
5,318 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.54 m/s, a=1.149 m/s²) | An object starts with initial velocity 20.54 m/s and experiences constant acceleration 1.149 m/s² for 11.15 s. Final velocity: v = v0 + a t = 20.54 + (1.149)(11.15) = 33.35 m/s. Displacement: s = v0 t + (1/2) a t² = 300.5 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. |
5,319 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.56 m/s, a=-2.451 m/s²) | An object starts with initial velocity 18.56 m/s and experiences constant acceleration -2.451 m/s² for 18.72 s. Final velocity: v = v0 + a t = 18.56 + (-2.451)(18.72) = -27.34 m/s. Displacement: s = v0 t + (1/2) a t² = -82.2 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. |
5,320 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.11 m/s, a=-2.848 m/s²) | An object starts with initial velocity 11.11 m/s and experiences constant acceleration -2.848 m/s² for 2.972 s. Final velocity: v = v0 + a t = 11.11 + (-2.848)(2.972) = 2.648 m/s. Displacement: s = v0 t + (1/2) a t² = 20.45 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. |
5,321 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.01 m/s, a=0.7182 m/s²) | An object starts with initial velocity 7.01 m/s and experiences constant acceleration 0.7182 m/s² for 11.69 s. Final velocity: v = v0 + a t = 7.01 + (0.7182)(11.69) = 15.41 m/s. Displacement: s = v0 t + (1/2) a t² = 131 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. |
5,322 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.41 m/s, a=6.53 m/s²) | An object starts with initial velocity 24.41 m/s and experiences constant acceleration 6.53 m/s² for 3.273 s. Final velocity: v = v0 + a t = 24.41 + (6.53)(3.273) = 45.79 m/s. Displacement: s = v0 t + (1/2) a t² = 114.9 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. |
5,323 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.736 m/s, a=4.424 m/s²) | An object starts with initial velocity 6.736 m/s and experiences constant acceleration 4.424 m/s² for 11.71 s. Final velocity: v = v0 + a t = 6.736 + (4.424)(11.71) = 58.54 m/s. Displacement: s = v0 t + (1/2) a t² = 382.2 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. |
5,324 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.218 m/s, a=4.733 m/s²) | An object starts with initial velocity 2.218 m/s and experiences constant acceleration 4.733 m/s² for 18.31 s. Final velocity: v = v0 + a t = 2.218 + (4.733)(18.31) = 88.86 m/s. Displacement: s = v0 t + (1/2) a t² = 833.6 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. |
5,325 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.12 m/s, a=4.672 m/s²) | An object starts with initial velocity 28.12 m/s and experiences constant acceleration 4.672 m/s² for 6.367 s. Final velocity: v = v0 + a t = 28.12 + (4.672)(6.367) = 57.86 m/s. Displacement: s = v0 t + (1/2) a t² = 273.7 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. |
5,326 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.48 m/s, a=1.745 m/s²) | An object starts with initial velocity 18.48 m/s and experiences constant acceleration 1.745 m/s² for 15.21 s. Final velocity: v = v0 + a t = 18.48 + (1.745)(15.21) = 45.03 m/s. Displacement: s = v0 t + (1/2) a t² = 483.1 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. |
5,327 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.49 m/s, a=4.189 m/s²) | An object starts with initial velocity 20.49 m/s and experiences constant acceleration 4.189 m/s² for 7.558 s. Final velocity: v = v0 + a t = 20.49 + (4.189)(7.558) = 52.15 m/s. Displacement: s = v0 t + (1/2) a t² = 274.5 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. |
5,328 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.64 m/s, a=1.825 m/s²) | An object starts with initial velocity 29.64 m/s and experiences constant acceleration 1.825 m/s² for 18.47 s. Final velocity: v = v0 + a t = 29.64 + (1.825)(18.47) = 63.34 m/s. Displacement: s = v0 t + (1/2) a t² = 858.6 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. |
5,329 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.594 m/s, a=3.047 m/s²) | An object starts with initial velocity 4.594 m/s and experiences constant acceleration 3.047 m/s² for 7.843 s. Final velocity: v = v0 + a t = 4.594 + (3.047)(7.843) = 28.49 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 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. |
5,330 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.332 m/s, a=4.556 m/s²) | An object starts with initial velocity 4.332 m/s and experiences constant acceleration 4.556 m/s² for 4.313 s. Final velocity: v = v0 + a t = 4.332 + (4.556)(4.313) = 23.98 m/s. Displacement: s = v0 t + (1/2) a t² = 61.06 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. |
5,331 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.02 m/s, a=9.987 m/s²) | An object starts with initial velocity 29.02 m/s and experiences constant acceleration 9.987 m/s² for 17.76 s. Final velocity: v = v0 + a t = 29.02 + (9.987)(17.76) = 206.4 m/s. Displacement: s = v0 t + (1/2) a t² = 2090 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. |
5,332 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.04 m/s, a=-4.686 m/s²) | An object starts with initial velocity 11.04 m/s and experiences constant acceleration -4.686 m/s² for 16.3 s. Final velocity: v = v0 + a t = 11.04 + (-4.686)(16.3) = -65.36 m/s. Displacement: s = v0 t + (1/2) a t² = -442.7 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. |
5,333 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.32 m/s, a=1.899 m/s²) | An object starts with initial velocity 4.32 m/s and experiences constant acceleration 1.899 m/s² for 14.5 s. Final velocity: v = v0 + a t = 4.32 + (1.899)(14.5) = 31.86 m/s. Displacement: s = v0 t + (1/2) a t² = 262.4 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. |
5,334 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.24 m/s, a=-1.595 m/s²) | An object starts with initial velocity 16.24 m/s and experiences constant acceleration -1.595 m/s² for 8.642 s. Final velocity: v = v0 + a t = 16.24 + (-1.595)(8.642) = 2.458 m/s. Displacement: s = v0 t + (1/2) a t² = 80.82 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. |
5,335 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.2 m/s, a=0.2941 m/s²) | An object starts with initial velocity 25.2 m/s and experiences constant acceleration 0.2941 m/s² for 18.9 s. Final velocity: v = v0 + a t = 25.2 + (0.2941)(18.9) = 30.76 m/s. Displacement: s = v0 t + (1/2) a t² = 528.8 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. |
5,336 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.63 m/s, a=1.266 m/s²) | An object starts with initial velocity 12.63 m/s and experiences constant acceleration 1.266 m/s² for 14.94 s. Final velocity: v = v0 + a t = 12.63 + (1.266)(14.94) = 31.54 m/s. Displacement: s = v0 t + (1/2) a t² = 329.9 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. |
5,337 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.32 m/s, a=0.8266 m/s²) | An object starts with initial velocity 13.32 m/s and experiences constant acceleration 0.8266 m/s² for 7.908 s. Final velocity: v = v0 + a t = 13.32 + (0.8266)(7.908) = 19.85 m/s. Displacement: s = v0 t + (1/2) a t² = 131.1 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. |
5,338 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.78 m/s, a=0.9832 m/s²) | An object starts with initial velocity 9.78 m/s and experiences constant acceleration 0.9832 m/s² for 14.74 s. Final velocity: v = v0 + a t = 9.78 + (0.9832)(14.74) = 24.28 m/s. Displacement: s = v0 t + (1/2) a t² = 251 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. |
5,339 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.177 m/s, a=-1.746 m/s²) | An object starts with initial velocity 6.177 m/s and experiences constant acceleration -1.746 m/s² for 4.628 s. Final velocity: v = v0 + a t = 6.177 + (-1.746)(4.628) = -1.902 m/s. Displacement: s = v0 t + (1/2) a t² = 9.895 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. |
5,340 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.838 m/s, a=8.104 m/s²) | An object starts with initial velocity 5.838 m/s and experiences constant acceleration 8.104 m/s² for 13.53 s. Final velocity: v = v0 + a t = 5.838 + (8.104)(13.53) = 115.5 m/s. Displacement: s = v0 t + (1/2) a t² = 820.4 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. |
5,341 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.57 m/s, a=8.505 m/s²) | An object starts with initial velocity 18.57 m/s and experiences constant acceleration 8.505 m/s² for 11.42 s. Final velocity: v = v0 + a t = 18.57 + (8.505)(11.42) = 115.7 m/s. Displacement: s = v0 t + (1/2) a t² = 766.2 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. |
5,342 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.92 m/s, a=1.123 m/s²) | An object starts with initial velocity 22.92 m/s and experiences constant acceleration 1.123 m/s² for 13.24 s. Final velocity: v = v0 + a t = 22.92 + (1.123)(13.24) = 37.78 m/s. Displacement: s = v0 t + (1/2) a t² = 401.7 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. |
5,343 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.405 m/s, a=-2.88 m/s²) | An object starts with initial velocity 6.405 m/s and experiences constant acceleration -2.88 m/s² for 3.064 s. Final velocity: v = v0 + a t = 6.405 + (-2.88)(3.064) = -2.42 m/s. Displacement: s = v0 t + (1/2) a t² = 6.106 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. |
5,344 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.57 m/s, a=-0.4952 m/s²) | An object starts with initial velocity 19.57 m/s and experiences constant acceleration -0.4952 m/s² for 16.82 s. Final velocity: v = v0 + a t = 19.57 + (-0.4952)(16.82) = 11.24 m/s. Displacement: s = v0 t + (1/2) a t² = 259.1 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. |
5,345 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.24 m/s, a=4.354 m/s²) | An object starts with initial velocity 23.24 m/s and experiences constant acceleration 4.354 m/s² for 1.967 s. Final velocity: v = v0 + a t = 23.24 + (4.354)(1.967) = 31.8 m/s. Displacement: s = v0 t + (1/2) a t² = 54.13 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. |
5,346 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.515 m/s, a=3.275 m/s²) | An object starts with initial velocity 6.515 m/s and experiences constant acceleration 3.275 m/s² for 3.978 s. Final velocity: v = v0 + a t = 6.515 + (3.275)(3.978) = 19.54 m/s. Displacement: s = v0 t + (1/2) a t² = 51.83 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. |
5,347 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.53 m/s, a=2.763 m/s²) | An object starts with initial velocity 11.53 m/s and experiences constant acceleration 2.763 m/s² for 4.426 s. Final velocity: v = v0 + a t = 11.53 + (2.763)(4.426) = 23.76 m/s. Displacement: s = v0 t + (1/2) a t² = 78.08 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. |
5,348 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.29 m/s, a=5.41 m/s²) | An object starts with initial velocity 13.29 m/s and experiences constant acceleration 5.41 m/s² for 8.333 s. Final velocity: v = v0 + a t = 13.29 + (5.41)(8.333) = 58.37 m/s. Displacement: s = v0 t + (1/2) a t² = 298.6 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. |
5,349 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.01 m/s, a=-0.9002 m/s²) | An object starts with initial velocity 20.01 m/s and experiences constant acceleration -0.9002 m/s² for 15.17 s. Final velocity: v = v0 + a t = 20.01 + (-0.9002)(15.17) = 6.351 m/s. Displacement: s = v0 t + (1/2) a t² = 200 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. |
5,350 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.9 m/s, a=-2.662 m/s²) | An object starts with initial velocity 16.9 m/s and experiences constant acceleration -2.662 m/s² for 8.636 s. Final velocity: v = v0 + a t = 16.9 + (-2.662)(8.636) = -6.089 m/s. Displacement: s = v0 t + (1/2) a t² = 46.69 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. |
5,351 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.46 m/s, a=-2.033 m/s²) | An object starts with initial velocity 23.46 m/s and experiences constant acceleration -2.033 m/s² for 8.815 s. Final velocity: v = v0 + a t = 23.46 + (-2.033)(8.815) = 5.537 m/s. Displacement: s = v0 t + (1/2) a t² = 127.8 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. |
5,352 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.06 m/s, a=8.02 m/s²) | An object starts with initial velocity 14.06 m/s and experiences constant acceleration 8.02 m/s² for 3.481 s. Final velocity: v = v0 + a t = 14.06 + (8.02)(3.481) = 41.97 m/s. Displacement: s = v0 t + (1/2) a t² = 97.51 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. |
5,353 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.94 m/s, a=-0.2568 m/s²) | An object starts with initial velocity 27.94 m/s and experiences constant acceleration -0.2568 m/s² for 18.73 s. Final velocity: v = v0 + a t = 27.94 + (-0.2568)(18.73) = 23.13 m/s. Displacement: s = v0 t + (1/2) a t² = 478.2 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. |
5,354 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.37 m/s, a=6.03 m/s²) | An object starts with initial velocity 18.37 m/s and experiences constant acceleration 6.03 m/s² for 17.64 s. Final velocity: v = v0 + a t = 18.37 + (6.03)(17.64) = 124.7 m/s. Displacement: s = v0 t + (1/2) a t² = 1262 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. |
5,355 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.29 m/s, a=6.804 m/s²) | An object starts with initial velocity 20.29 m/s and experiences constant acceleration 6.804 m/s² for 2.629 s. Final velocity: v = v0 + a t = 20.29 + (6.804)(2.629) = 38.18 m/s. Displacement: s = v0 t + (1/2) a t² = 76.86 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. |
5,356 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.2601 m/s, a=7.934 m/s²) | An object starts with initial velocity 0.2601 m/s and experiences constant acceleration 7.934 m/s² for 2.002 s. Final velocity: v = v0 + a t = 0.2601 + (7.934)(2.002) = 16.15 m/s. Displacement: s = v0 t + (1/2) a t² = 16.42 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. |
5,357 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.58 m/s, a=-0.3006 m/s²) | An object starts with initial velocity 25.58 m/s and experiences constant acceleration -0.3006 m/s² for 18.13 s. Final velocity: v = v0 + a t = 25.58 + (-0.3006)(18.13) = 20.13 m/s. Displacement: s = v0 t + (1/2) a t² = 414.4 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. |
5,358 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.09 m/s, a=-2.741 m/s²) | An object starts with initial velocity 6.09 m/s and experiences constant acceleration -2.741 m/s² for 5.047 s. Final velocity: v = v0 + a t = 6.09 + (-2.741)(5.047) = -7.744 m/s. Displacement: s = v0 t + (1/2) a t² = -4.174 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. |
5,359 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.22 m/s, a=0.4441 m/s²) | An object starts with initial velocity 25.22 m/s and experiences constant acceleration 0.4441 m/s² for 18.28 s. Final velocity: v = v0 + a t = 25.22 + (0.4441)(18.28) = 33.34 m/s. Displacement: s = v0 t + (1/2) a t² = 535.1 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. |
5,360 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=17.5 m/s, a=7.424 m/s²) | An object starts with initial velocity 17.5 m/s and experiences constant acceleration 7.424 m/s² for 10.03 s. Final velocity: v = v0 + a t = 17.5 + (7.424)(10.03) = 91.94 m/s. Displacement: s = v0 t + (1/2) a t² = 548.7 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. |
5,361 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.11 m/s, a=-0.6539 m/s²) | An object starts with initial velocity 21.11 m/s and experiences constant acceleration -0.6539 m/s² for 2.928 s. Final velocity: v = v0 + a t = 21.11 + (-0.6539)(2.928) = 19.19 m/s. Displacement: s = v0 t + (1/2) a t² = 59.01 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. |
5,362 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.86 m/s, a=8.512 m/s²) | An object starts with initial velocity 16.86 m/s and experiences constant acceleration 8.512 m/s² for 3.888 s. Final velocity: v = v0 + a t = 16.86 + (8.512)(3.888) = 49.96 m/s. Displacement: s = v0 t + (1/2) a t² = 129.9 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. |
5,363 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.46 m/s, a=2.985 m/s²) | An object starts with initial velocity 12.46 m/s and experiences constant acceleration 2.985 m/s² for 12.75 s. Final velocity: v = v0 + a t = 12.46 + (2.985)(12.75) = 50.5 m/s. Displacement: s = v0 t + (1/2) a t² = 401.3 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. |
5,364 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.748 m/s, a=3.285 m/s²) | An object starts with initial velocity 4.748 m/s and experiences constant acceleration 3.285 m/s² for 9.922 s. Final velocity: v = v0 + a t = 4.748 + (3.285)(9.922) = 37.34 m/s. Displacement: s = v0 t + (1/2) a t² = 208.8 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. |
5,365 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.5 m/s, a=5.349 m/s²) | An object starts with initial velocity 29.5 m/s and experiences constant acceleration 5.349 m/s² for 18.17 s. Final velocity: v = v0 + a t = 29.5 + (5.349)(18.17) = 126.7 m/s. Displacement: s = v0 t + (1/2) a t² = 1419 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. |
5,366 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.28 m/s, a=4.958 m/s²) | An object starts with initial velocity 29.28 m/s and experiences constant acceleration 4.958 m/s² for 3.786 s. Final velocity: v = v0 + a t = 29.28 + (4.958)(3.786) = 48.06 m/s. Displacement: s = v0 t + (1/2) a t² = 146.4 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. |
5,367 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.35 m/s, a=6.335 m/s²) | An object starts with initial velocity 13.35 m/s and experiences constant acceleration 6.335 m/s² for 3.576 s. Final velocity: v = v0 + a t = 13.35 + (6.335)(3.576) = 36 m/s. Displacement: s = v0 t + (1/2) a t² = 88.25 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. |
5,368 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.43 m/s, a=0.6905 m/s²) | An object starts with initial velocity 11.43 m/s and experiences constant acceleration 0.6905 m/s² for 4.239 s. Final velocity: v = v0 + a t = 11.43 + (0.6905)(4.239) = 14.36 m/s. Displacement: s = v0 t + (1/2) a t² = 54.65 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. |
5,369 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.5986 m/s, a=5.322 m/s²) | An object starts with initial velocity 0.5986 m/s and experiences constant acceleration 5.322 m/s² for 16.54 s. Final velocity: v = v0 + a t = 0.5986 + (5.322)(16.54) = 88.63 m/s. Displacement: s = v0 t + (1/2) a t² = 737.9 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. |
5,370 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.93 m/s, a=3.773 m/s²) | An object starts with initial velocity 27.93 m/s and experiences constant acceleration 3.773 m/s² for 4.455 s. Final velocity: v = v0 + a t = 27.93 + (3.773)(4.455) = 44.74 m/s. Displacement: s = v0 t + (1/2) a t² = 161.9 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. |
5,371 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.82 m/s, a=9.554 m/s²) | An object starts with initial velocity 26.82 m/s and experiences constant acceleration 9.554 m/s² for 18.99 s. Final velocity: v = v0 + a t = 26.82 + (9.554)(18.99) = 208.2 m/s. Displacement: s = v0 t + (1/2) a t² = 2231 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. |
5,372 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=17 m/s, a=8.284 m/s²) | An object starts with initial velocity 17 m/s and experiences constant acceleration 8.284 m/s² for 19.77 s. Final velocity: v = v0 + a t = 17 + (8.284)(19.77) = 180.8 m/s. Displacement: s = v0 t + (1/2) a t² = 1955 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. |
5,373 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.59 m/s, a=-3.967 m/s²) | An object starts with initial velocity 26.59 m/s and experiences constant acceleration -3.967 m/s² for 3.564 s. Final velocity: v = v0 + a t = 26.59 + (-3.967)(3.564) = 12.46 m/s. Displacement: s = v0 t + (1/2) a t² = 69.59 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. |
5,374 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.003 m/s, a=0.9042 m/s²) | An object starts with initial velocity 9.003 m/s and experiences constant acceleration 0.9042 m/s² for 3.84 s. Final velocity: v = v0 + a t = 9.003 + (0.9042)(3.84) = 12.48 m/s. Displacement: s = v0 t + (1/2) a t² = 41.24 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. |
5,375 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.79 m/s, a=6.865 m/s²) | An object starts with initial velocity 29.79 m/s and experiences constant acceleration 6.865 m/s² for 13.71 s. Final velocity: v = v0 + a t = 29.79 + (6.865)(13.71) = 123.9 m/s. Displacement: s = v0 t + (1/2) a t² = 1053 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. |
5,376 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.85 m/s, a=-0.1895 m/s²) | An object starts with initial velocity 28.85 m/s and experiences constant acceleration -0.1895 m/s² for 14.52 s. Final velocity: v = v0 + a t = 28.85 + (-0.1895)(14.52) = 26.1 m/s. Displacement: s = v0 t + (1/2) a t² = 398.8 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. |
5,377 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.46 m/s, a=-3.754 m/s²) | An object starts with initial velocity 28.46 m/s and experiences constant acceleration -3.754 m/s² for 12.45 s. Final velocity: v = v0 + a t = 28.46 + (-3.754)(12.45) = -18.29 m/s. Displacement: s = v0 t + (1/2) a t² = 63.37 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. |
5,378 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.98 m/s, a=-4.761 m/s²) | An object starts with initial velocity 23.98 m/s and experiences constant acceleration -4.761 m/s² for 17.93 s. Final velocity: v = v0 + a t = 23.98 + (-4.761)(17.93) = -61.38 m/s. Displacement: s = v0 t + (1/2) a t² = -335.3 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. |
5,379 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.53 m/s, a=-2.464 m/s²) | An object starts with initial velocity 12.53 m/s and experiences constant acceleration -2.464 m/s² for 17.17 s. Final velocity: v = v0 + a t = 12.53 + (-2.464)(17.17) = -29.79 m/s. Displacement: s = v0 t + (1/2) a t² = -148.2 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. |
5,380 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.761 m/s, a=-0.7963 m/s²) | An object starts with initial velocity 5.761 m/s and experiences constant acceleration -0.7963 m/s² for 10.89 s. Final velocity: v = v0 + a t = 5.761 + (-0.7963)(10.89) = -2.91 m/s. Displacement: s = v0 t + (1/2) a t² = 15.52 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. |
5,381 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.48 m/s, a=2.344 m/s²) | An object starts with initial velocity 27.48 m/s and experiences constant acceleration 2.344 m/s² for 18.21 s. Final velocity: v = v0 + a t = 27.48 + (2.344)(18.21) = 70.17 m/s. Displacement: s = v0 t + (1/2) a t² = 889.1 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. |
5,382 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.56 m/s, a=-1.418 m/s²) | An object starts with initial velocity 1.56 m/s and experiences constant acceleration -1.418 m/s² for 6.826 s. Final velocity: v = v0 + a t = 1.56 + (-1.418)(6.826) = -8.119 m/s. Displacement: s = v0 t + (1/2) a t² = -22.38 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. |
5,383 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.47 m/s, a=1.494 m/s²) | An object starts with initial velocity 13.47 m/s and experiences constant acceleration 1.494 m/s² for 1.769 s. Final velocity: v = v0 + a t = 13.47 + (1.494)(1.769) = 16.11 m/s. Displacement: s = v0 t + (1/2) a t² = 26.16 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. |
5,384 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.5 m/s, a=6.396 m/s²) | An object starts with initial velocity 22.5 m/s and experiences constant acceleration 6.396 m/s² for 9.704 s. Final velocity: v = v0 + a t = 22.5 + (6.396)(9.704) = 84.57 m/s. Displacement: s = v0 t + (1/2) a t² = 519.5 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. |
5,385 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.407 m/s, a=3.269 m/s²) | An object starts with initial velocity 2.407 m/s and experiences constant acceleration 3.269 m/s² for 3.482 s. Final velocity: v = v0 + a t = 2.407 + (3.269)(3.482) = 13.79 m/s. Displacement: s = v0 t + (1/2) a t² = 28.2 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. |
5,386 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.35 m/s, a=4.363 m/s²) | An object starts with initial velocity 29.35 m/s and experiences constant acceleration 4.363 m/s² for 14.96 s. Final velocity: v = v0 + a t = 29.35 + (4.363)(14.96) = 94.6 m/s. Displacement: s = v0 t + (1/2) a t² = 927 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. |
5,387 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.5764 m/s, a=0.7101 m/s²) | An object starts with initial velocity 0.5764 m/s and experiences constant acceleration 0.7101 m/s² for 18.19 s. Final velocity: v = v0 + a t = 0.5764 + (0.7101)(18.19) = 13.49 m/s. Displacement: s = v0 t + (1/2) a t² = 127.9 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. |
5,388 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.4 m/s, a=-4.46 m/s²) | An object starts with initial velocity 11.4 m/s and experiences constant acceleration -4.46 m/s² for 13.77 s. Final velocity: v = v0 + a t = 11.4 + (-4.46)(13.77) = -50 m/s. Displacement: s = v0 t + (1/2) a t² = -265.7 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. |
5,389 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.91 m/s, a=0.03452 m/s²) | An object starts with initial velocity 20.91 m/s and experiences constant acceleration 0.03452 m/s² for 16.26 s. Final velocity: v = v0 + a t = 20.91 + (0.03452)(16.26) = 21.47 m/s. Displacement: s = v0 t + (1/2) a t² = 344.5 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. |
5,390 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.61 m/s, a=6.762 m/s²) | An object starts with initial velocity 25.61 m/s and experiences constant acceleration 6.762 m/s² for 8.737 s. Final velocity: v = v0 + a t = 25.61 + (6.762)(8.737) = 84.68 m/s. Displacement: s = v0 t + (1/2) a t² = 481.8 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. |
5,391 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.26 m/s, a=9.144 m/s²) | An object starts with initial velocity 10.26 m/s and experiences constant acceleration 9.144 m/s² for 14.66 s. Final velocity: v = v0 + a t = 10.26 + (9.144)(14.66) = 144.3 m/s. Displacement: s = v0 t + (1/2) a t² = 1133 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. |
5,392 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.57 m/s, a=2.332 m/s²) | An object starts with initial velocity 16.57 m/s and experiences constant acceleration 2.332 m/s² for 6.067 s. Final velocity: v = v0 + a t = 16.57 + (2.332)(6.067) = 30.72 m/s. Displacement: s = v0 t + (1/2) a t² = 143.5 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. |
5,393 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.4 m/s, a=8.782 m/s²) | An object starts with initial velocity 27.4 m/s and experiences constant acceleration 8.782 m/s² for 2.611 s. Final velocity: v = v0 + a t = 27.4 + (8.782)(2.611) = 50.33 m/s. Displacement: s = v0 t + (1/2) a t² = 101.5 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. |
5,394 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.99 m/s, a=-0.2208 m/s²) | An object starts with initial velocity 19.99 m/s and experiences constant acceleration -0.2208 m/s² for 10.67 s. Final velocity: v = v0 + a t = 19.99 + (-0.2208)(10.67) = 17.63 m/s. Displacement: s = v0 t + (1/2) a t² = 200.6 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. |
5,395 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.406 m/s, a=7.161 m/s²) | An object starts with initial velocity 3.406 m/s and experiences constant acceleration 7.161 m/s² for 16.32 s. Final velocity: v = v0 + a t = 3.406 + (7.161)(16.32) = 120.3 m/s. Displacement: s = v0 t + (1/2) a t² = 1009 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. |
5,396 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.211 m/s, a=-3.884 m/s²) | An object starts with initial velocity 3.211 m/s and experiences constant acceleration -3.884 m/s² for 8.094 s. Final velocity: v = v0 + a t = 3.211 + (-3.884)(8.094) = -28.23 m/s. Displacement: s = v0 t + (1/2) a t² = -101.2 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. |
5,397 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.62 m/s, a=7.022 m/s²) | An object starts with initial velocity 4.62 m/s and experiences constant acceleration 7.022 m/s² for 15.8 s. Final velocity: v = v0 + a t = 4.62 + (7.022)(15.8) = 115.6 m/s. Displacement: s = v0 t + (1/2) a t² = 949.3 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. |
5,398 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.91 m/s, a=-4.855 m/s²) | An object starts with initial velocity 25.91 m/s and experiences constant acceleration -4.855 m/s² for 1.255 s. Final velocity: v = v0 + a t = 25.91 + (-4.855)(1.255) = 19.81 m/s. Displacement: s = v0 t + (1/2) a t² = 28.7 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. |
5,399 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.21 m/s, a=8.052 m/s²) | An object starts with initial velocity 24.21 m/s and experiences constant acceleration 8.052 m/s² for 12.73 s. Final velocity: v = v0 + a t = 24.21 + (8.052)(12.73) = 126.7 m/s. Displacement: s = v0 t + (1/2) a t² = 960.9 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. |
5,400 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.687 m/s, a=4.392 m/s²) | An object starts with initial velocity 4.687 m/s and experiences constant acceleration 4.392 m/s² for 17.56 s. Final velocity: v = v0 + a t = 4.687 + (4.392)(17.56) = 81.79 m/s. Displacement: s = v0 t + (1/2) a t² = 759.1 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. |
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