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values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
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7,001 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.26 m/s, a=1.377 m/s²) | An object starts with initial velocity 18.26 m/s and experiences constant acceleration 1.377 m/s² for 5.608 s. Final velocity: v = v0 + a t = 18.26 + (1.377)(5.608) = 25.98 m/s. Displacement: s = v0 t + (1/2) a t² = 124 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. |
7,002 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.47 m/s, a=-1.129 m/s²) | An object starts with initial velocity 23.47 m/s and experiences constant acceleration -1.129 m/s² for 8.684 s. Final velocity: v = v0 + a t = 23.47 + (-1.129)(8.684) = 13.67 m/s. Displacement: s = v0 t + (1/2) a t² = 161.2 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. |
7,003 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.44 m/s, a=-3.038 m/s²) | An object starts with initial velocity 11.44 m/s and experiences constant acceleration -3.038 m/s² for 13.04 s. Final velocity: v = v0 + a t = 11.44 + (-3.038)(13.04) = -28.17 m/s. Displacement: s = v0 t + (1/2) a t² = -109.1 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. |
7,004 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.11 m/s, a=0.04761 m/s²) | An object starts with initial velocity 23.11 m/s and experiences constant acceleration 0.04761 m/s² for 6.495 s. Final velocity: v = v0 + a t = 23.11 + (0.04761)(6.495) = 23.42 m/s. Displacement: s = v0 t + (1/2) a t² = 151.1 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. |
7,005 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.252 m/s, a=4.489 m/s²) | An object starts with initial velocity 3.252 m/s and experiences constant acceleration 4.489 m/s² for 12.47 s. Final velocity: v = v0 + a t = 3.252 + (4.489)(12.47) = 59.23 m/s. Displacement: s = v0 t + (1/2) a t² = 389.6 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. |
7,006 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.41 m/s, a=8.88 m/s²) | An object starts with initial velocity 10.41 m/s and experiences constant acceleration 8.88 m/s² for 1.174 s. Final velocity: v = v0 + a t = 10.41 + (8.88)(1.174) = 20.84 m/s. Displacement: s = v0 t + (1/2) a t² = 18.34 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. |
7,007 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.96 m/s, a=1.382 m/s²) | An object starts with initial velocity 27.96 m/s and experiences constant acceleration 1.382 m/s² for 17.26 s. Final velocity: v = v0 + a t = 27.96 + (1.382)(17.26) = 51.81 m/s. Displacement: s = v0 t + (1/2) a t² = 688.3 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. |
7,008 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.552 m/s, a=-2.718 m/s²) | An object starts with initial velocity 3.552 m/s and experiences constant acceleration -2.718 m/s² for 4.44 s. Final velocity: v = v0 + a t = 3.552 + (-2.718)(4.44) = -8.514 m/s. Displacement: s = v0 t + (1/2) a t² = -11.01 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. |
7,009 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.86 m/s, a=1.779 m/s²) | An object starts with initial velocity 22.86 m/s and experiences constant acceleration 1.779 m/s² for 19.32 s. Final velocity: v = v0 + a t = 22.86 + (1.779)(19.32) = 57.23 m/s. Displacement: s = v0 t + (1/2) a t² = 773.8 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. |
7,010 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.35 m/s, a=4.85 m/s²) | An object starts with initial velocity 14.35 m/s and experiences constant acceleration 4.85 m/s² for 6.902 s. Final velocity: v = v0 + a t = 14.35 + (4.85)(6.902) = 47.82 m/s. Displacement: s = v0 t + (1/2) a t² = 214.5 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. |
7,011 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.03 m/s, a=-0.2599 m/s²) | An object starts with initial velocity 4.03 m/s and experiences constant acceleration -0.2599 m/s² for 2.279 s. Final velocity: v = v0 + a t = 4.03 + (-0.2599)(2.279) = 3.438 m/s. Displacement: s = v0 t + (1/2) a t² = 8.511 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. |
7,012 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.8325 m/s, a=-3.814 m/s²) | An object starts with initial velocity 0.8325 m/s and experiences constant acceleration -3.814 m/s² for 6.338 s. Final velocity: v = v0 + a t = 0.8325 + (-3.814)(6.338) = -23.34 m/s. Displacement: s = v0 t + (1/2) a t² = -71.32 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. |
7,013 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.5 m/s, a=-3.615 m/s²) | An object starts with initial velocity 29.5 m/s and experiences constant acceleration -3.615 m/s² for 18.3 s. Final velocity: v = v0 + a t = 29.5 + (-3.615)(18.3) = -36.67 m/s. Displacement: s = v0 t + (1/2) a t² = -65.59 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. |
7,014 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.55 m/s, a=7.229 m/s²) | An object starts with initial velocity 25.55 m/s and experiences constant acceleration 7.229 m/s² for 5.773 s. Final velocity: v = v0 + a t = 25.55 + (7.229)(5.773) = 67.29 m/s. Displacement: s = v0 t + (1/2) a t² = 268 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. |
7,015 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.91 m/s, a=4.591 m/s²) | An object starts with initial velocity 23.91 m/s and experiences constant acceleration 4.591 m/s² for 19.87 s. Final velocity: v = v0 + a t = 23.91 + (4.591)(19.87) = 115.2 m/s. Displacement: s = v0 t + (1/2) a t² = 1382 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. |
7,016 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.1836 m/s, a=8.567 m/s²) | An object starts with initial velocity 0.1836 m/s and experiences constant acceleration 8.567 m/s² for 11.2 s. Final velocity: v = v0 + a t = 0.1836 + (8.567)(11.2) = 96.13 m/s. Displacement: s = v0 t + (1/2) a t² = 539.4 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. |
7,017 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.25 m/s, a=3.832 m/s²) | An object starts with initial velocity 3.25 m/s and experiences constant acceleration 3.832 m/s² for 19.66 s. Final velocity: v = v0 + a t = 3.25 + (3.832)(19.66) = 78.58 m/s. Displacement: s = v0 t + (1/2) a t² = 804.3 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. |
7,018 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.44 m/s, a=2.418 m/s²) | An object starts with initial velocity 14.44 m/s and experiences constant acceleration 2.418 m/s² for 11.62 s. Final velocity: v = v0 + a t = 14.44 + (2.418)(11.62) = 42.53 m/s. Displacement: s = v0 t + (1/2) a t² = 330.9 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. |
7,019 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.877 m/s, a=-3.813 m/s²) | An object starts with initial velocity 5.877 m/s and experiences constant acceleration -3.813 m/s² for 11.98 s. Final velocity: v = v0 + a t = 5.877 + (-3.813)(11.98) = -39.8 m/s. Displacement: s = v0 t + (1/2) a t² = -203.2 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. |
7,020 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.47 m/s, a=0.3755 m/s²) | An object starts with initial velocity 26.47 m/s and experiences constant acceleration 0.3755 m/s² for 18.68 s. Final velocity: v = v0 + a t = 26.47 + (0.3755)(18.68) = 33.49 m/s. Displacement: s = v0 t + (1/2) a t² = 560.2 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. |
7,021 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.92 m/s, a=8.965 m/s²) | An object starts with initial velocity 26.92 m/s and experiences constant acceleration 8.965 m/s² for 6.191 s. Final velocity: v = v0 + a t = 26.92 + (8.965)(6.191) = 82.42 m/s. Displacement: s = v0 t + (1/2) a t² = 338.4 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. |
7,022 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.047 m/s, a=5.774 m/s²) | An object starts with initial velocity 4.047 m/s and experiences constant acceleration 5.774 m/s² for 16.06 s. Final velocity: v = v0 + a t = 4.047 + (5.774)(16.06) = 96.77 m/s. Displacement: s = v0 t + (1/2) a t² = 809.5 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. |
7,023 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.58 m/s, a=4.579 m/s²) | An object starts with initial velocity 25.58 m/s and experiences constant acceleration 4.579 m/s² for 9.075 s. Final velocity: v = v0 + a t = 25.58 + (4.579)(9.075) = 67.13 m/s. Displacement: s = v0 t + (1/2) a t² = 420.7 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. |
7,024 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.418 m/s, a=-3.336 m/s²) | An object starts with initial velocity 4.418 m/s and experiences constant acceleration -3.336 m/s² for 4.128 s. Final velocity: v = v0 + a t = 4.418 + (-3.336)(4.128) = -9.354 m/s. Displacement: s = v0 t + (1/2) a t² = -10.19 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. |
7,025 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.117 m/s, a=-1.232 m/s²) | An object starts with initial velocity 6.117 m/s and experiences constant acceleration -1.232 m/s² for 14.97 s. Final velocity: v = v0 + a t = 6.117 + (-1.232)(14.97) = -12.32 m/s. Displacement: s = v0 t + (1/2) a t² = -46.47 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. |
7,026 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.53 m/s, a=0.1323 m/s²) | An object starts with initial velocity 26.53 m/s and experiences constant acceleration 0.1323 m/s² for 9.172 s. Final velocity: v = v0 + a t = 26.53 + (0.1323)(9.172) = 27.75 m/s. Displacement: s = v0 t + (1/2) a t² = 248.9 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. |
7,027 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.89 m/s, a=5.942 m/s²) | An object starts with initial velocity 20.89 m/s and experiences constant acceleration 5.942 m/s² for 17.46 s. Final velocity: v = v0 + a t = 20.89 + (5.942)(17.46) = 124.7 m/s. Displacement: s = v0 t + (1/2) a t² = 1271 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. |
7,028 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.97 m/s, a=1.918 m/s²) | An object starts with initial velocity 15.97 m/s and experiences constant acceleration 1.918 m/s² for 7.657 s. Final velocity: v = v0 + a t = 15.97 + (1.918)(7.657) = 30.65 m/s. Displacement: s = v0 t + (1/2) a t² = 178.5 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. |
7,029 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.57 m/s, a=-2.468 m/s²) | An object starts with initial velocity 24.57 m/s and experiences constant acceleration -2.468 m/s² for 19.68 s. Final velocity: v = v0 + a t = 24.57 + (-2.468)(19.68) = -24.01 m/s. Displacement: s = v0 t + (1/2) a t² = 5.507 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. |
7,030 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.44 m/s, a=-2.378 m/s²) | An object starts with initial velocity 28.44 m/s and experiences constant acceleration -2.378 m/s² for 3.43 s. Final velocity: v = v0 + a t = 28.44 + (-2.378)(3.43) = 20.28 m/s. Displacement: s = v0 t + (1/2) a t² = 83.57 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. |
7,031 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.15 m/s, a=5.421 m/s²) | An object starts with initial velocity 20.15 m/s and experiences constant acceleration 5.421 m/s² for 5.419 s. Final velocity: v = v0 + a t = 20.15 + (5.421)(5.419) = 49.53 m/s. Displacement: s = v0 t + (1/2) a t² = 188.8 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. |
7,032 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.729 m/s, a=-1.202 m/s²) | An object starts with initial velocity 9.729 m/s and experiences constant acceleration -1.202 m/s² for 16.14 s. Final velocity: v = v0 + a t = 9.729 + (-1.202)(16.14) = -9.669 m/s. Displacement: s = v0 t + (1/2) a t² = 0.4865 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. |
7,033 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.4 m/s, a=-0.9747 m/s²) | An object starts with initial velocity 29.4 m/s and experiences constant acceleration -0.9747 m/s² for 1.597 s. Final velocity: v = v0 + a t = 29.4 + (-0.9747)(1.597) = 27.84 m/s. Displacement: s = v0 t + (1/2) a t² = 45.71 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. |
7,034 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.34 m/s, a=-1.183 m/s²) | An object starts with initial velocity 28.34 m/s and experiences constant acceleration -1.183 m/s² for 13.4 s. Final velocity: v = v0 + a t = 28.34 + (-1.183)(13.4) = 12.48 m/s. Displacement: s = v0 t + (1/2) a t² = 273.6 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. |
7,035 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.556 m/s, a=2.008 m/s²) | An object starts with initial velocity 8.556 m/s and experiences constant acceleration 2.008 m/s² for 15.06 s. Final velocity: v = v0 + a t = 8.556 + (2.008)(15.06) = 38.79 m/s. Displacement: s = v0 t + (1/2) a t² = 356.4 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. |
7,036 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.1 m/s, a=7.683 m/s²) | An object starts with initial velocity 26.1 m/s and experiences constant acceleration 7.683 m/s² for 2.457 s. Final velocity: v = v0 + a t = 26.1 + (7.683)(2.457) = 44.98 m/s. Displacement: s = v0 t + (1/2) a t² = 87.32 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. |
7,037 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.198 m/s, a=-2.097 m/s²) | An object starts with initial velocity 4.198 m/s and experiences constant acceleration -2.097 m/s² for 18.76 s. Final velocity: v = v0 + a t = 4.198 + (-2.097)(18.76) = -35.13 m/s. Displacement: s = v0 t + (1/2) a t² = -290.1 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. |
7,038 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.54 m/s, a=-0.718 m/s²) | An object starts with initial velocity 29.54 m/s and experiences constant acceleration -0.718 m/s² for 11.21 s. Final velocity: v = v0 + a t = 29.54 + (-0.718)(11.21) = 21.49 m/s. Displacement: s = v0 t + (1/2) a t² = 286 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. |
7,039 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.96 m/s, a=5.965 m/s²) | An object starts with initial velocity 22.96 m/s and experiences constant acceleration 5.965 m/s² for 10.33 s. Final velocity: v = v0 + a t = 22.96 + (5.965)(10.33) = 84.6 m/s. Displacement: s = v0 t + (1/2) a t² = 555.7 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. |
7,040 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.2 m/s, a=6.002 m/s²) | An object starts with initial velocity 28.2 m/s and experiences constant acceleration 6.002 m/s² for 19.68 s. Final velocity: v = v0 + a t = 28.2 + (6.002)(19.68) = 146.3 m/s. Displacement: s = v0 t + (1/2) a t² = 1718 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. |
7,041 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.52 m/s, a=8.518 m/s²) | An object starts with initial velocity 13.52 m/s and experiences constant acceleration 8.518 m/s² for 8.565 s. Final velocity: v = v0 + a t = 13.52 + (8.518)(8.565) = 86.47 m/s. Displacement: s = v0 t + (1/2) a t² = 428.2 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. |
7,042 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.188 m/s, a=4.967 m/s²) | An object starts with initial velocity 6.188 m/s and experiences constant acceleration 4.967 m/s² for 13.26 s. Final velocity: v = v0 + a t = 6.188 + (4.967)(13.26) = 72.04 m/s. Displacement: s = v0 t + (1/2) a t² = 518.5 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. |
7,043 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.36 m/s, a=-2.505 m/s²) | An object starts with initial velocity 20.36 m/s and experiences constant acceleration -2.505 m/s² for 4.225 s. Final velocity: v = v0 + a t = 20.36 + (-2.505)(4.225) = 9.774 m/s. Displacement: s = v0 t + (1/2) a t² = 63.64 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. |
7,044 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.749 m/s, a=7.489 m/s²) | An object starts with initial velocity 5.749 m/s and experiences constant acceleration 7.489 m/s² for 11.24 s. Final velocity: v = v0 + a t = 5.749 + (7.489)(11.24) = 89.92 m/s. Displacement: s = v0 t + (1/2) a t² = 537.6 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. |
7,045 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.55 m/s, a=7.295 m/s²) | An object starts with initial velocity 20.55 m/s and experiences constant acceleration 7.295 m/s² for 18.06 s. Final velocity: v = v0 + a t = 20.55 + (7.295)(18.06) = 152.3 m/s. Displacement: s = v0 t + (1/2) a t² = 1560 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. |
7,046 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.61 m/s, a=-4.811 m/s²) | An object starts with initial velocity 10.61 m/s and experiences constant acceleration -4.811 m/s² for 11.32 s. Final velocity: v = v0 + a t = 10.61 + (-4.811)(11.32) = -43.83 m/s. Displacement: s = v0 t + (1/2) a t² = -187.9 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. |
7,047 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.04 m/s, a=-3.991 m/s²) | An object starts with initial velocity 24.04 m/s and experiences constant acceleration -3.991 m/s² for 15.9 s. Final velocity: v = v0 + a t = 24.04 + (-3.991)(15.9) = -39.41 m/s. Displacement: s = v0 t + (1/2) a t² = -122.2 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. |
7,048 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.87 m/s, a=7.401 m/s²) | An object starts with initial velocity 28.87 m/s and experiences constant acceleration 7.401 m/s² for 5.844 s. Final velocity: v = v0 + a t = 28.87 + (7.401)(5.844) = 72.12 m/s. Displacement: s = v0 t + (1/2) a t² = 295.1 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. |
7,049 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.44 m/s, a=-2.085 m/s²) | An object starts with initial velocity 21.44 m/s and experiences constant acceleration -2.085 m/s² for 8.346 s. Final velocity: v = v0 + a t = 21.44 + (-2.085)(8.346) = 4.046 m/s. Displacement: s = v0 t + (1/2) a t² = 106.4 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. |
7,050 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.83 m/s, a=9.683 m/s²) | An object starts with initial velocity 29.83 m/s and experiences constant acceleration 9.683 m/s² for 7.175 s. Final velocity: v = v0 + a t = 29.83 + (9.683)(7.175) = 99.3 m/s. Displacement: s = v0 t + (1/2) a t² = 463.3 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. |
7,051 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.36 m/s, a=7.446 m/s²) | An object starts with initial velocity 16.36 m/s and experiences constant acceleration 7.446 m/s² for 6.069 s. Final velocity: v = v0 + a t = 16.36 + (7.446)(6.069) = 61.55 m/s. Displacement: s = v0 t + (1/2) a t² = 236.4 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. |
7,052 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.81 m/s, a=-0.03464 m/s²) | An object starts with initial velocity 26.81 m/s and experiences constant acceleration -0.03464 m/s² for 5.361 s. Final velocity: v = v0 + a t = 26.81 + (-0.03464)(5.361) = 26.63 m/s. Displacement: s = v0 t + (1/2) a t² = 143.2 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. |
7,053 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.168 m/s, a=-4.464 m/s²) | An object starts with initial velocity 9.168 m/s and experiences constant acceleration -4.464 m/s² for 18.5 s. Final velocity: v = v0 + a t = 9.168 + (-4.464)(18.5) = -73.39 m/s. Displacement: s = v0 t + (1/2) a t² = -593.9 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. |
7,054 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21 m/s, a=4.516 m/s²) | An object starts with initial velocity 21 m/s and experiences constant acceleration 4.516 m/s² for 2.973 s. Final velocity: v = v0 + a t = 21 + (4.516)(2.973) = 34.42 m/s. Displacement: s = v0 t + (1/2) a t² = 82.39 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. |
7,055 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.074 m/s, a=8.089 m/s²) | An object starts with initial velocity 2.074 m/s and experiences constant acceleration 8.089 m/s² for 9.37 s. Final velocity: v = v0 + a t = 2.074 + (8.089)(9.37) = 77.87 m/s. Displacement: s = v0 t + (1/2) a t² = 374.5 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. |
7,056 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.15 m/s, a=2.713 m/s²) | An object starts with initial velocity 15.15 m/s and experiences constant acceleration 2.713 m/s² for 2.272 s. Final velocity: v = v0 + a t = 15.15 + (2.713)(2.272) = 21.32 m/s. Displacement: s = v0 t + (1/2) a t² = 41.44 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. |
7,057 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.75 m/s, a=9.833 m/s²) | An object starts with initial velocity 12.75 m/s and experiences constant acceleration 9.833 m/s² for 6.298 s. Final velocity: v = v0 + a t = 12.75 + (9.833)(6.298) = 74.68 m/s. Displacement: s = v0 t + (1/2) a t² = 275.3 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. |
7,058 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.632 m/s, a=5.05 m/s²) | An object starts with initial velocity 7.632 m/s and experiences constant acceleration 5.05 m/s² for 7.83 s. Final velocity: v = v0 + a t = 7.632 + (5.05)(7.83) = 47.18 m/s. Displacement: s = v0 t + (1/2) a t² = 214.6 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. |
7,059 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.857 m/s, a=-4.198 m/s²) | An object starts with initial velocity 7.857 m/s and experiences constant acceleration -4.198 m/s² for 11.1 s. Final velocity: v = v0 + a t = 7.857 + (-4.198)(11.1) = -38.75 m/s. Displacement: s = v0 t + (1/2) a t² = -171.5 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. |
7,060 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.58 m/s, a=8.185 m/s²) | An object starts with initial velocity 24.58 m/s and experiences constant acceleration 8.185 m/s² for 14.08 s. Final velocity: v = v0 + a t = 24.58 + (8.185)(14.08) = 139.8 m/s. Displacement: s = v0 t + (1/2) a t² = 1158 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. |
7,061 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.25 m/s, a=4.293 m/s²) | An object starts with initial velocity 14.25 m/s and experiences constant acceleration 4.293 m/s² for 9.556 s. Final velocity: v = v0 + a t = 14.25 + (4.293)(9.556) = 55.28 m/s. Displacement: s = v0 t + (1/2) a t² = 332.2 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. |
7,062 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.53 m/s, a=-3.393 m/s²) | An object starts with initial velocity 23.53 m/s and experiences constant acceleration -3.393 m/s² for 13.19 s. Final velocity: v = v0 + a t = 23.53 + (-3.393)(13.19) = -21.23 m/s. Displacement: s = v0 t + (1/2) a t² = 15.13 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. |
7,063 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.53 m/s, a=8.655 m/s²) | An object starts with initial velocity 19.53 m/s and experiences constant acceleration 8.655 m/s² for 14.79 s. Final velocity: v = v0 + a t = 19.53 + (8.655)(14.79) = 147.6 m/s. Displacement: s = v0 t + (1/2) a t² = 1236 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. |
7,064 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.615 m/s, a=4.655 m/s²) | An object starts with initial velocity 9.615 m/s and experiences constant acceleration 4.655 m/s² for 3.343 s. Final velocity: v = v0 + a t = 9.615 + (4.655)(3.343) = 25.18 m/s. Displacement: s = v0 t + (1/2) a t² = 58.16 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. |
7,065 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.1 m/s, a=9.405 m/s²) | An object starts with initial velocity 16.1 m/s and experiences constant acceleration 9.405 m/s² for 10.74 s. Final velocity: v = v0 + a t = 16.1 + (9.405)(10.74) = 117.1 m/s. Displacement: s = v0 t + (1/2) a t² = 715 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. |
7,066 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.664 m/s, a=3.083 m/s²) | An object starts with initial velocity 7.664 m/s and experiences constant acceleration 3.083 m/s² for 8.334 s. Final velocity: v = v0 + a t = 7.664 + (3.083)(8.334) = 33.36 m/s. Displacement: s = v0 t + (1/2) a t² = 170.9 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. |
7,067 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.66 m/s, a=3.689 m/s²) | An object starts with initial velocity 18.66 m/s and experiences constant acceleration 3.689 m/s² for 19.78 s. Final velocity: v = v0 + a t = 18.66 + (3.689)(19.78) = 91.62 m/s. Displacement: s = v0 t + (1/2) a t² = 1090 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. |
7,068 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.83 m/s, a=6.646 m/s²) | An object starts with initial velocity 15.83 m/s and experiences constant acceleration 6.646 m/s² for 17.81 s. Final velocity: v = v0 + a t = 15.83 + (6.646)(17.81) = 134.2 m/s. Displacement: s = v0 t + (1/2) a t² = 1336 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. |
7,069 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.93 m/s, a=3.983 m/s²) | An object starts with initial velocity 22.93 m/s and experiences constant acceleration 3.983 m/s² for 6.815 s. Final velocity: v = v0 + a t = 22.93 + (3.983)(6.815) = 50.07 m/s. Displacement: s = v0 t + (1/2) a t² = 248.8 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. |
7,070 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.56 m/s, a=2.219 m/s²) | An object starts with initial velocity 29.56 m/s and experiences constant acceleration 2.219 m/s² for 14.36 s. Final velocity: v = v0 + a t = 29.56 + (2.219)(14.36) = 61.41 m/s. Displacement: s = v0 t + (1/2) a t² = 653.1 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. |
7,071 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.13 m/s, a=-3.43 m/s²) | An object starts with initial velocity 25.13 m/s and experiences constant acceleration -3.43 m/s² for 16.96 s. Final velocity: v = v0 + a t = 25.13 + (-3.43)(16.96) = -33.03 m/s. Displacement: s = v0 t + (1/2) a t² = -67.05 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. |
7,072 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.43 m/s, a=-1.193 m/s²) | An object starts with initial velocity 20.43 m/s and experiences constant acceleration -1.193 m/s² for 5.418 s. Final velocity: v = v0 + a t = 20.43 + (-1.193)(5.418) = 13.97 m/s. Displacement: s = v0 t + (1/2) a t² = 93.19 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. |
7,073 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.31 m/s, a=7.928 m/s²) | An object starts with initial velocity 24.31 m/s and experiences constant acceleration 7.928 m/s² for 19.74 s. Final velocity: v = v0 + a t = 24.31 + (7.928)(19.74) = 180.8 m/s. Displacement: s = v0 t + (1/2) a t² = 2025 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. |
7,074 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.21 m/s, a=9.453 m/s²) | An object starts with initial velocity 16.21 m/s and experiences constant acceleration 9.453 m/s² for 14.5 s. Final velocity: v = v0 + a t = 16.21 + (9.453)(14.5) = 153.3 m/s. Displacement: s = v0 t + (1/2) a t² = 1229 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. |
7,075 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.251 m/s, a=-3.017 m/s²) | An object starts with initial velocity 5.251 m/s and experiences constant acceleration -3.017 m/s² for 4.871 s. Final velocity: v = v0 + a t = 5.251 + (-3.017)(4.871) = -9.445 m/s. Displacement: s = v0 t + (1/2) a t² = -10.21 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. |
7,076 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.7 m/s, a=-1.604 m/s²) | An object starts with initial velocity 16.7 m/s and experiences constant acceleration -1.604 m/s² for 9.541 s. Final velocity: v = v0 + a t = 16.7 + (-1.604)(9.541) = 1.396 m/s. Displacement: s = v0 t + (1/2) a t² = 86.34 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. |
7,077 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.64 m/s, a=-1.426 m/s²) | An object starts with initial velocity 15.64 m/s and experiences constant acceleration -1.426 m/s² for 16.05 s. Final velocity: v = v0 + a t = 15.64 + (-1.426)(16.05) = -7.25 m/s. Displacement: s = v0 t + (1/2) a t² = 67.38 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. |
7,078 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.528 m/s, a=-3.309 m/s²) | An object starts with initial velocity 4.528 m/s and experiences constant acceleration -3.309 m/s² for 13.28 s. Final velocity: v = v0 + a t = 4.528 + (-3.309)(13.28) = -39.4 m/s. Displacement: s = v0 t + (1/2) a t² = -231.5 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. |
7,079 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.49 m/s, a=-4.549 m/s²) | An object starts with initial velocity 16.49 m/s and experiences constant acceleration -4.549 m/s² for 18.48 s. Final velocity: v = v0 + a t = 16.49 + (-4.549)(18.48) = -67.57 m/s. Displacement: s = v0 t + (1/2) a t² = -471.9 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. |
7,080 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.713 m/s, a=8.223 m/s²) | An object starts with initial velocity 4.713 m/s and experiences constant acceleration 8.223 m/s² for 4.992 s. Final velocity: v = v0 + a t = 4.713 + (8.223)(4.992) = 45.76 m/s. Displacement: s = v0 t + (1/2) a t² = 126 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. |
7,081 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.172 m/s, a=8.004 m/s²) | An object starts with initial velocity 5.172 m/s and experiences constant acceleration 8.004 m/s² for 18.56 s. Final velocity: v = v0 + a t = 5.172 + (8.004)(18.56) = 153.7 m/s. Displacement: s = v0 t + (1/2) a t² = 1474 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. |
7,082 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.35 m/s, a=3.356 m/s²) | An object starts with initial velocity 21.35 m/s and experiences constant acceleration 3.356 m/s² for 5.03 s. Final velocity: v = v0 + a t = 21.35 + (3.356)(5.03) = 38.23 m/s. Displacement: s = v0 t + (1/2) a t² = 149.8 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. |
7,083 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.371 m/s, a=-4.328 m/s²) | An object starts with initial velocity 4.371 m/s and experiences constant acceleration -4.328 m/s² for 3.222 s. Final velocity: v = v0 + a t = 4.371 + (-4.328)(3.222) = -9.577 m/s. Displacement: s = v0 t + (1/2) a t² = -8.387 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. |
7,084 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.553 m/s, a=-2.364 m/s²) | An object starts with initial velocity 5.553 m/s and experiences constant acceleration -2.364 m/s² for 1.04 s. Final velocity: v = v0 + a t = 5.553 + (-2.364)(1.04) = 3.094 m/s. Displacement: s = v0 t + (1/2) a t² = 4.498 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. |
7,085 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.891 m/s, a=2.83 m/s²) | An object starts with initial velocity 1.891 m/s and experiences constant acceleration 2.83 m/s² for 9.765 s. Final velocity: v = v0 + a t = 1.891 + (2.83)(9.765) = 29.53 m/s. Displacement: s = v0 t + (1/2) a t² = 153.4 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. |
7,086 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.38 m/s, a=-4.32 m/s²) | An object starts with initial velocity 11.38 m/s and experiences constant acceleration -4.32 m/s² for 1.566 s. Final velocity: v = v0 + a t = 11.38 + (-4.32)(1.566) = 4.615 m/s. Displacement: s = v0 t + (1/2) a t² = 12.53 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. |
7,087 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.24 m/s, a=3.953 m/s²) | An object starts with initial velocity 25.24 m/s and experiences constant acceleration 3.953 m/s² for 17.49 s. Final velocity: v = v0 + a t = 25.24 + (3.953)(17.49) = 94.37 m/s. Displacement: s = v0 t + (1/2) a t² = 1046 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. |
7,088 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.59 m/s, a=5.151 m/s²) | An object starts with initial velocity 27.59 m/s and experiences constant acceleration 5.151 m/s² for 14.58 s. Final velocity: v = v0 + a t = 27.59 + (5.151)(14.58) = 102.7 m/s. Displacement: s = v0 t + (1/2) a t² = 950 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. |
7,089 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.651 m/s, a=3.216 m/s²) | An object starts with initial velocity 3.651 m/s and experiences constant acceleration 3.216 m/s² for 16.54 s. Final velocity: v = v0 + a t = 3.651 + (3.216)(16.54) = 56.84 m/s. Displacement: s = v0 t + (1/2) a t² = 500.2 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. |
7,090 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.681 m/s, a=0.7557 m/s²) | An object starts with initial velocity 5.681 m/s and experiences constant acceleration 0.7557 m/s² for 2.766 s. Final velocity: v = v0 + a t = 5.681 + (0.7557)(2.766) = 7.771 m/s. Displacement: s = v0 t + (1/2) a t² = 18.6 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. |
7,091 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.851 m/s, a=5.868 m/s²) | An object starts with initial velocity 1.851 m/s and experiences constant acceleration 5.868 m/s² for 18.06 s. Final velocity: v = v0 + a t = 1.851 + (5.868)(18.06) = 107.8 m/s. Displacement: s = v0 t + (1/2) a t² = 990 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. |
7,092 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.681 m/s, a=-0.2101 m/s²) | An object starts with initial velocity 8.681 m/s and experiences constant acceleration -0.2101 m/s² for 5.635 s. Final velocity: v = v0 + a t = 8.681 + (-0.2101)(5.635) = 7.497 m/s. Displacement: s = v0 t + (1/2) a t² = 45.58 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. |
7,093 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.3 m/s, a=3.844 m/s²) | An object starts with initial velocity 28.3 m/s and experiences constant acceleration 3.844 m/s² for 15.35 s. Final velocity: v = v0 + a t = 28.3 + (3.844)(15.35) = 87.3 m/s. Displacement: s = v0 t + (1/2) a t² = 887.1 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. |
7,094 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.59 m/s, a=-0.8545 m/s²) | An object starts with initial velocity 23.59 m/s and experiences constant acceleration -0.8545 m/s² for 15.88 s. Final velocity: v = v0 + a t = 23.59 + (-0.8545)(15.88) = 10.02 m/s. Displacement: s = v0 t + (1/2) a t² = 266.8 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. |
7,095 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.99 m/s, a=3.255 m/s²) | An object starts with initial velocity 22.99 m/s and experiences constant acceleration 3.255 m/s² for 3.627 s. Final velocity: v = v0 + a t = 22.99 + (3.255)(3.627) = 34.8 m/s. Displacement: s = v0 t + (1/2) a t² = 104.8 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. |
7,096 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.446 m/s, a=1.13 m/s²) | An object starts with initial velocity 9.446 m/s and experiences constant acceleration 1.13 m/s² for 19.67 s. Final velocity: v = v0 + a t = 9.446 + (1.13)(19.67) = 31.67 m/s. Displacement: s = v0 t + (1/2) a t² = 404.3 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. |
7,097 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.492 m/s, a=5.144 m/s²) | An object starts with initial velocity 9.492 m/s and experiences constant acceleration 5.144 m/s² for 2.856 s. Final velocity: v = v0 + a t = 9.492 + (5.144)(2.856) = 24.18 m/s. Displacement: s = v0 t + (1/2) a t² = 48.08 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. |
7,098 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.1095 m/s, a=6 m/s²) | An object starts with initial velocity 0.1095 m/s and experiences constant acceleration 6 m/s² for 19.9 s. Final velocity: v = v0 + a t = 0.1095 + (6)(19.9) = 119.5 m/s. Displacement: s = v0 t + (1/2) a t² = 1190 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. |
7,099 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.71 m/s, a=6.274 m/s²) | An object starts with initial velocity 13.71 m/s and experiences constant acceleration 6.274 m/s² for 18.4 s. Final velocity: v = v0 + a t = 13.71 + (6.274)(18.4) = 129.2 m/s. Displacement: s = v0 t + (1/2) a t² = 1315 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. |
7,100 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.1052 m/s, a=7.261 m/s²) | An object starts with initial velocity 0.1052 m/s and experiences constant acceleration 7.261 m/s² for 6.3 s. Final velocity: v = v0 + a t = 0.1052 + (7.261)(6.3) = 45.85 m/s. Displacement: s = v0 t + (1/2) a t² = 144.7 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. |
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