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values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
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3,601 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.18 m/s, a=2.705 m/s²) | An object starts with initial velocity 25.18 m/s and experiences constant acceleration 2.705 m/s² for 19.1 s. Final velocity: v = v0 + a t = 25.18 + (2.705)(19.1) = 76.85 m/s. Displacement: s = v0 t + (1/2) a t² = 974.2 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. |
3,602 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.68 m/s, a=0.6864 m/s²) | An object starts with initial velocity 12.68 m/s and experiences constant acceleration 0.6864 m/s² for 8.092 s. Final velocity: v = v0 + a t = 12.68 + (0.6864)(8.092) = 18.24 m/s. Displacement: s = v0 t + (1/2) a t² = 125.1 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. |
3,603 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.397 m/s, a=8.711 m/s²) | An object starts with initial velocity 3.397 m/s and experiences constant acceleration 8.711 m/s² for 5.746 s. Final velocity: v = v0 + a t = 3.397 + (8.711)(5.746) = 53.44 m/s. Displacement: s = v0 t + (1/2) a t² = 163.3 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. |
3,604 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.17 m/s, a=6.496 m/s²) | An object starts with initial velocity 16.17 m/s and experiences constant acceleration 6.496 m/s² for 3.239 s. Final velocity: v = v0 + a t = 16.17 + (6.496)(3.239) = 37.22 m/s. Displacement: s = v0 t + (1/2) a t² = 86.48 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. |
3,605 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.975 m/s, a=-0.5968 m/s²) | An object starts with initial velocity 8.975 m/s and experiences constant acceleration -0.5968 m/s² for 5.048 s. Final velocity: v = v0 + a t = 8.975 + (-0.5968)(5.048) = 5.962 m/s. Displacement: s = v0 t + (1/2) a t² = 37.7 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
3,606 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.14 m/s, a=3.533 m/s²) | An object starts with initial velocity 22.14 m/s and experiences constant acceleration 3.533 m/s² for 5.132 s. Final velocity: v = v0 + a t = 22.14 + (3.533)(5.132) = 40.27 m/s. Displacement: s = v0 t + (1/2) a t² = 160.1 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. |
3,607 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.145 m/s, a=8.997 m/s²) | An object starts with initial velocity 9.145 m/s and experiences constant acceleration 8.997 m/s² for 13.22 s. Final velocity: v = v0 + a t = 9.145 + (8.997)(13.22) = 128 m/s. Displacement: s = v0 t + (1/2) a t² = 906.6 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. |
3,608 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.77 m/s, a=-4.469 m/s²) | An object starts with initial velocity 24.77 m/s and experiences constant acceleration -4.469 m/s² for 9.798 s. Final velocity: v = v0 + a t = 24.77 + (-4.469)(9.798) = -19.01 m/s. Displacement: s = v0 t + (1/2) a t² = 28.22 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. |
3,609 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.53 m/s, a=2.324 m/s²) | An object starts with initial velocity 18.53 m/s and experiences constant acceleration 2.324 m/s² for 7.759 s. Final velocity: v = v0 + a t = 18.53 + (2.324)(7.759) = 36.56 m/s. Displacement: s = v0 t + (1/2) a t² = 213.8 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. |
3,610 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.47 m/s, a=-0.07172 m/s²) | An object starts with initial velocity 18.47 m/s and experiences constant acceleration -0.07172 m/s² for 7.724 s. Final velocity: v = v0 + a t = 18.47 + (-0.07172)(7.724) = 17.91 m/s. Displacement: s = v0 t + (1/2) a t² = 140.5 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. |
3,611 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.1546 m/s, a=8.353 m/s²) | An object starts with initial velocity 0.1546 m/s and experiences constant acceleration 8.353 m/s² for 4.537 s. Final velocity: v = v0 + a t = 0.1546 + (8.353)(4.537) = 38.05 m/s. Displacement: s = v0 t + (1/2) a t² = 86.67 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. |
3,612 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.64 m/s, a=-3.48 m/s²) | An object starts with initial velocity 10.64 m/s and experiences constant acceleration -3.48 m/s² for 10.35 s. Final velocity: v = v0 + a t = 10.64 + (-3.48)(10.35) = -25.38 m/s. Displacement: s = v0 t + (1/2) a t² = -76.28 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. |
3,613 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.542 m/s, a=2.715 m/s²) | An object starts with initial velocity 2.542 m/s and experiences constant acceleration 2.715 m/s² for 3.921 s. Final velocity: v = v0 + a t = 2.542 + (2.715)(3.921) = 13.19 m/s. Displacement: s = v0 t + (1/2) a t² = 30.83 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. |
3,614 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.715 m/s, a=2.311 m/s²) | An object starts with initial velocity 3.715 m/s and experiences constant acceleration 2.311 m/s² for 3.957 s. Final velocity: v = v0 + a t = 3.715 + (2.311)(3.957) = 12.86 m/s. Displacement: s = v0 t + (1/2) a t² = 32.8 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. |
3,615 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.7 m/s, a=-1.609 m/s²) | An object starts with initial velocity 19.7 m/s and experiences constant acceleration -1.609 m/s² for 8.512 s. Final velocity: v = v0 + a t = 19.7 + (-1.609)(8.512) = 6.007 m/s. Displacement: s = v0 t + (1/2) a t² = 109.4 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. |
3,616 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.979 m/s, a=1.425 m/s²) | An object starts with initial velocity 8.979 m/s and experiences constant acceleration 1.425 m/s² for 4.461 s. Final velocity: v = v0 + a t = 8.979 + (1.425)(4.461) = 15.34 m/s. Displacement: s = v0 t + (1/2) a t² = 54.24 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. |
3,617 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.35 m/s, a=-3.37 m/s²) | An object starts with initial velocity 24.35 m/s and experiences constant acceleration -3.37 m/s² for 9.333 s. Final velocity: v = v0 + a t = 24.35 + (-3.37)(9.333) = -7.101 m/s. Displacement: s = v0 t + (1/2) a t² = 80.47 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. |
3,618 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.18 m/s, a=-2.572 m/s²) | An object starts with initial velocity 25.18 m/s and experiences constant acceleration -2.572 m/s² for 7.721 s. Final velocity: v = v0 + a t = 25.18 + (-2.572)(7.721) = 5.319 m/s. Displacement: s = v0 t + (1/2) a t² = 117.7 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. |
3,619 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.02 m/s, a=0.3886 m/s²) | An object starts with initial velocity 13.02 m/s and experiences constant acceleration 0.3886 m/s² for 17.54 s. Final velocity: v = v0 + a t = 13.02 + (0.3886)(17.54) = 19.83 m/s. Displacement: s = v0 t + (1/2) a t² = 288.1 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. |
3,620 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.954 m/s, a=-2.156 m/s²) | An object starts with initial velocity 5.954 m/s and experiences constant acceleration -2.156 m/s² for 1.765 s. Final velocity: v = v0 + a t = 5.954 + (-2.156)(1.765) = 2.148 m/s. Displacement: s = v0 t + (1/2) a t² = 7.149 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. |
3,621 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.84 m/s, a=6.159 m/s²) | An object starts with initial velocity 11.84 m/s and experiences constant acceleration 6.159 m/s² for 18.12 s. Final velocity: v = v0 + a t = 11.84 + (6.159)(18.12) = 123.4 m/s. Displacement: s = v0 t + (1/2) a t² = 1225 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. |
3,622 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.809 m/s, a=-2.015 m/s²) | An object starts with initial velocity 4.809 m/s and experiences constant acceleration -2.015 m/s² for 10.11 s. Final velocity: v = v0 + a t = 4.809 + (-2.015)(10.11) = -15.56 m/s. Displacement: s = v0 t + (1/2) a t² = -54.31 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. |
3,623 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.96 m/s, a=-1.013 m/s²) | An object starts with initial velocity 19.96 m/s and experiences constant acceleration -1.013 m/s² for 9.001 s. Final velocity: v = v0 + a t = 19.96 + (-1.013)(9.001) = 10.84 m/s. Displacement: s = v0 t + (1/2) a t² = 138.6 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. |
3,624 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.5 m/s, a=6.997 m/s²) | An object starts with initial velocity 16.5 m/s and experiences constant acceleration 6.997 m/s² for 14.57 s. Final velocity: v = v0 + a t = 16.5 + (6.997)(14.57) = 118.5 m/s. Displacement: s = v0 t + (1/2) a t² = 983.4 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. |
3,625 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.747 m/s, a=6.466 m/s²) | An object starts with initial velocity 9.747 m/s and experiences constant acceleration 6.466 m/s² for 17.75 s. Final velocity: v = v0 + a t = 9.747 + (6.466)(17.75) = 124.5 m/s. Displacement: s = v0 t + (1/2) a t² = 1192 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. |
3,626 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.06 m/s, a=8.853 m/s²) | An object starts with initial velocity 15.06 m/s and experiences constant acceleration 8.853 m/s² for 17.02 s. Final velocity: v = v0 + a t = 15.06 + (8.853)(17.02) = 165.7 m/s. Displacement: s = v0 t + (1/2) a t² = 1538 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. |
3,627 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.67 m/s, a=-3.354 m/s²) | An object starts with initial velocity 11.67 m/s and experiences constant acceleration -3.354 m/s² for 3.05 s. Final velocity: v = v0 + a t = 11.67 + (-3.354)(3.05) = 1.437 m/s. Displacement: s = v0 t + (1/2) a t² = 19.98 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. |
3,628 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.6346 m/s, a=-2.667 m/s²) | An object starts with initial velocity 0.6346 m/s and experiences constant acceleration -2.667 m/s² for 10.5 s. Final velocity: v = v0 + a t = 0.6346 + (-2.667)(10.5) = -27.37 m/s. Displacement: s = v0 t + (1/2) a t² = -140.3 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. |
3,629 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.02 m/s, a=-1.452 m/s²) | An object starts with initial velocity 23.02 m/s and experiences constant acceleration -1.452 m/s² for 13.89 s. Final velocity: v = v0 + a t = 23.02 + (-1.452)(13.89) = 2.85 m/s. Displacement: s = v0 t + (1/2) a t² = 179.7 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. |
3,630 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.26 m/s, a=9.647 m/s²) | An object starts with initial velocity 10.26 m/s and experiences constant acceleration 9.647 m/s² for 15.01 s. Final velocity: v = v0 + a t = 10.26 + (9.647)(15.01) = 155.1 m/s. Displacement: s = v0 t + (1/2) a t² = 1241 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. |
3,631 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.03 m/s, a=-0.658 m/s²) | An object starts with initial velocity 13.03 m/s and experiences constant acceleration -0.658 m/s² for 10.23 s. Final velocity: v = v0 + a t = 13.03 + (-0.658)(10.23) = 6.297 m/s. Displacement: s = v0 t + (1/2) a t² = 98.88 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. |
3,632 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.83 m/s, a=-1.284 m/s²) | An object starts with initial velocity 22.83 m/s and experiences constant acceleration -1.284 m/s² for 3.897 s. Final velocity: v = v0 + a t = 22.83 + (-1.284)(3.897) = 17.82 m/s. Displacement: s = v0 t + (1/2) a t² = 79.22 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. |
3,633 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.34 m/s, a=-1.258 m/s²) | An object starts with initial velocity 15.34 m/s and experiences constant acceleration -1.258 m/s² for 15.57 s. Final velocity: v = v0 + a t = 15.34 + (-1.258)(15.57) = -4.247 m/s. Displacement: s = v0 t + (1/2) a t² = 86.32 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. |
3,634 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.93 m/s, a=9.914 m/s²) | An object starts with initial velocity 25.93 m/s and experiences constant acceleration 9.914 m/s² for 5.7 s. Final velocity: v = v0 + a t = 25.93 + (9.914)(5.7) = 82.43 m/s. Displacement: s = v0 t + (1/2) a t² = 308.8 m. These relations follow directly from the definitions of average velocity and constant acceleration. | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
3,635 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.62 m/s, a=-2.024 m/s²) | An object starts with initial velocity 24.62 m/s and experiences constant acceleration -2.024 m/s² for 14.42 s. Final velocity: v = v0 + a t = 24.62 + (-2.024)(14.42) = -4.571 m/s. Displacement: s = v0 t + (1/2) a t² = 144.6 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. |
3,636 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.3 m/s, a=5.517 m/s²) | An object starts with initial velocity 24.3 m/s and experiences constant acceleration 5.517 m/s² for 10.54 s. Final velocity: v = v0 + a t = 24.3 + (5.517)(10.54) = 82.47 m/s. Displacement: s = v0 t + (1/2) a t² = 562.9 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. |
3,637 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.436 m/s, a=9.888 m/s²) | An object starts with initial velocity 5.436 m/s and experiences constant acceleration 9.888 m/s² for 12.23 s. Final velocity: v = v0 + a t = 5.436 + (9.888)(12.23) = 126.4 m/s. Displacement: s = v0 t + (1/2) a t² = 806.3 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. |
3,638 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.03 m/s, a=-1.559 m/s²) | An object starts with initial velocity 19.03 m/s and experiences constant acceleration -1.559 m/s² for 3.514 s. Final velocity: v = v0 + a t = 19.03 + (-1.559)(3.514) = 13.56 m/s. Displacement: s = v0 t + (1/2) a t² = 57.25 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. |
3,639 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.151 m/s, a=9.856 m/s²) | An object starts with initial velocity 1.151 m/s and experiences constant acceleration 9.856 m/s² for 18.65 s. Final velocity: v = v0 + a t = 1.151 + (9.856)(18.65) = 185 m/s. Displacement: s = v0 t + (1/2) a t² = 1736 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. |
3,640 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.79 m/s, a=4.247 m/s²) | An object starts with initial velocity 12.79 m/s and experiences constant acceleration 4.247 m/s² for 2.728 s. Final velocity: v = v0 + a t = 12.79 + (4.247)(2.728) = 24.37 m/s. Displacement: s = v0 t + (1/2) a t² = 50.69 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. |
3,641 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.529 m/s, a=1.109 m/s²) | An object starts with initial velocity 1.529 m/s and experiences constant acceleration 1.109 m/s² for 6.822 s. Final velocity: v = v0 + a t = 1.529 + (1.109)(6.822) = 9.098 m/s. Displacement: s = v0 t + (1/2) a t² = 36.25 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. |
3,642 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19 m/s, a=-1.529 m/s²) | An object starts with initial velocity 19 m/s and experiences constant acceleration -1.529 m/s² for 7.387 s. Final velocity: v = v0 + a t = 19 + (-1.529)(7.387) = 7.707 m/s. Displacement: s = v0 t + (1/2) a t² = 98.65 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. |
3,643 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.38 m/s, a=2.648 m/s²) | An object starts with initial velocity 14.38 m/s and experiences constant acceleration 2.648 m/s² for 13.23 s. Final velocity: v = v0 + a t = 14.38 + (2.648)(13.23) = 49.42 m/s. Displacement: s = v0 t + (1/2) a t² = 422.1 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. |
3,644 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.129 m/s, a=-0.9613 m/s²) | An object starts with initial velocity 9.129 m/s and experiences constant acceleration -0.9613 m/s² for 6.331 s. Final velocity: v = v0 + a t = 9.129 + (-0.9613)(6.331) = 3.043 m/s. Displacement: s = v0 t + (1/2) a t² = 38.53 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. |
3,645 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.53 m/s, a=1.271 m/s²) | An object starts with initial velocity 10.53 m/s and experiences constant acceleration 1.271 m/s² for 7.077 s. Final velocity: v = v0 + a t = 10.53 + (1.271)(7.077) = 19.53 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 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. |
3,646 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.427 m/s, a=-4.387 m/s²) | An object starts with initial velocity 1.427 m/s and experiences constant acceleration -4.387 m/s² for 1.99 s. Final velocity: v = v0 + a t = 1.427 + (-4.387)(1.99) = -7.305 m/s. Displacement: s = v0 t + (1/2) a t² = -5.85 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. |
3,647 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.34 m/s, a=-1.82 m/s²) | An object starts with initial velocity 22.34 m/s and experiences constant acceleration -1.82 m/s² for 9.969 s. Final velocity: v = v0 + a t = 22.34 + (-1.82)(9.969) = 4.196 m/s. Displacement: s = v0 t + (1/2) a t² = 132.3 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. |
3,648 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.25 m/s, a=-3.489 m/s²) | An object starts with initial velocity 27.25 m/s and experiences constant acceleration -3.489 m/s² for 4.512 s. Final velocity: v = v0 + a t = 27.25 + (-3.489)(4.512) = 11.51 m/s. Displacement: s = v0 t + (1/2) a t² = 87.46 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. |
3,649 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.45 m/s, a=0.4537 m/s²) | An object starts with initial velocity 28.45 m/s and experiences constant acceleration 0.4537 m/s² for 6.783 s. Final velocity: v = v0 + a t = 28.45 + (0.4537)(6.783) = 31.53 m/s. Displacement: s = v0 t + (1/2) a t² = 203.4 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. |
3,650 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.907 m/s, a=-4.795 m/s²) | An object starts with initial velocity 2.907 m/s and experiences constant acceleration -4.795 m/s² for 11.48 s. Final velocity: v = v0 + a t = 2.907 + (-4.795)(11.48) = -52.16 m/s. Displacement: s = v0 t + (1/2) a t² = -282.8 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. |
3,651 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.86 m/s, a=-0.03182 m/s²) | An object starts with initial velocity 25.86 m/s and experiences constant acceleration -0.03182 m/s² for 15.08 s. Final velocity: v = v0 + a t = 25.86 + (-0.03182)(15.08) = 25.38 m/s. Displacement: s = v0 t + (1/2) a t² = 386.5 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. |
3,652 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.84 m/s, a=6.682 m/s²) | An object starts with initial velocity 10.84 m/s and experiences constant acceleration 6.682 m/s² for 11.05 s. Final velocity: v = v0 + a t = 10.84 + (6.682)(11.05) = 84.67 m/s. Displacement: s = v0 t + (1/2) a t² = 527.6 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. |
3,653 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.15 m/s, a=4.754 m/s²) | An object starts with initial velocity 11.15 m/s and experiences constant acceleration 4.754 m/s² for 4.991 s. Final velocity: v = v0 + a t = 11.15 + (4.754)(4.991) = 34.87 m/s. Displacement: s = v0 t + (1/2) a t² = 114.8 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. |
3,654 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.52 m/s, a=8.308 m/s²) | An object starts with initial velocity 11.52 m/s and experiences constant acceleration 8.308 m/s² for 3.479 s. Final velocity: v = v0 + a t = 11.52 + (8.308)(3.479) = 40.43 m/s. Displacement: s = v0 t + (1/2) a t² = 90.37 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
3,655 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.28 m/s, a=-3.195 m/s²) | An object starts with initial velocity 22.28 m/s and experiences constant acceleration -3.195 m/s² for 12.14 s. Final velocity: v = v0 + a t = 22.28 + (-3.195)(12.14) = -16.52 m/s. Displacement: s = v0 t + (1/2) a t² = 34.96 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. |
3,656 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.37 m/s, a=4.815 m/s²) | An object starts with initial velocity 27.37 m/s and experiences constant acceleration 4.815 m/s² for 4.618 s. Final velocity: v = v0 + a t = 27.37 + (4.815)(4.618) = 49.6 m/s. Displacement: s = v0 t + (1/2) a t² = 177.7 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. |
3,657 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.14 m/s, a=8.883 m/s²) | An object starts with initial velocity 21.14 m/s and experiences constant acceleration 8.883 m/s² for 2.423 s. Final velocity: v = v0 + a t = 21.14 + (8.883)(2.423) = 42.66 m/s. Displacement: s = v0 t + (1/2) a t² = 77.28 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. |
3,658 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.4 m/s, a=0.1435 m/s²) | An object starts with initial velocity 16.4 m/s and experiences constant acceleration 0.1435 m/s² for 14.78 s. Final velocity: v = v0 + a t = 16.4 + (0.1435)(14.78) = 18.52 m/s. Displacement: s = v0 t + (1/2) a t² = 258.1 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. |
3,659 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.69 m/s, a=-1.97 m/s²) | An object starts with initial velocity 29.69 m/s and experiences constant acceleration -1.97 m/s² for 14.69 s. Final velocity: v = v0 + a t = 29.69 + (-1.97)(14.69) = 0.7407 m/s. Displacement: s = v0 t + (1/2) a t² = 223.6 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. |
3,660 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.314 m/s, a=-2.124 m/s²) | An object starts with initial velocity 1.314 m/s and experiences constant acceleration -2.124 m/s² for 11.46 s. Final velocity: v = v0 + a t = 1.314 + (-2.124)(11.46) = -23.03 m/s. Displacement: s = v0 t + (1/2) a t² = -124.4 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. |
3,661 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.576 m/s, a=8.156 m/s²) | An object starts with initial velocity 7.576 m/s and experiences constant acceleration 8.156 m/s² for 17.22 s. Final velocity: v = v0 + a t = 7.576 + (8.156)(17.22) = 148 m/s. Displacement: s = v0 t + (1/2) a t² = 1339 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. |
3,662 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.2 m/s, a=9.627 m/s²) | An object starts with initial velocity 27.2 m/s and experiences constant acceleration 9.627 m/s² for 18 s. Final velocity: v = v0 + a t = 27.2 + (9.627)(18) = 200.5 m/s. Displacement: s = v0 t + (1/2) a t² = 2050 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. |
3,663 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.45 m/s, a=5.76 m/s²) | An object starts with initial velocity 13.45 m/s and experiences constant acceleration 5.76 m/s² for 18.31 s. Final velocity: v = v0 + a t = 13.45 + (5.76)(18.31) = 118.9 m/s. Displacement: s = v0 t + (1/2) a t² = 1211 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. |
3,664 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.031 m/s, a=1.285 m/s²) | An object starts with initial velocity 2.031 m/s and experiences constant acceleration 1.285 m/s² for 18.7 s. Final velocity: v = v0 + a t = 2.031 + (1.285)(18.7) = 26.06 m/s. Displacement: s = v0 t + (1/2) a t² = 262.5 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. |
3,665 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.12 m/s, a=-4.672 m/s²) | An object starts with initial velocity 15.12 m/s and experiences constant acceleration -4.672 m/s² for 12.38 s. Final velocity: v = v0 + a t = 15.12 + (-4.672)(12.38) = -42.74 m/s. Displacement: s = v0 t + (1/2) a t² = -171 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. |
3,666 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.9 m/s, a=-3.066 m/s²) | An object starts with initial velocity 20.9 m/s and experiences constant acceleration -3.066 m/s² for 1.863 s. Final velocity: v = v0 + a t = 20.9 + (-3.066)(1.863) = 15.19 m/s. Displacement: s = v0 t + (1/2) a t² = 33.63 m. These relations follow directly from the definitions of average velocity and constant accelerat... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
3,667 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.99 m/s, a=6.916 m/s²) | An object starts with initial velocity 16.99 m/s and experiences constant acceleration 6.916 m/s² for 14.18 s. Final velocity: v = v0 + a t = 16.99 + (6.916)(14.18) = 115.1 m/s. Displacement: s = v0 t + (1/2) a t² = 936.4 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. |
3,668 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.22 m/s, a=0.9624 m/s²) | An object starts with initial velocity 22.22 m/s and experiences constant acceleration 0.9624 m/s² for 14.01 s. Final velocity: v = v0 + a t = 22.22 + (0.9624)(14.01) = 35.7 m/s. Displacement: s = v0 t + (1/2) a t² = 405.7 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. |
3,669 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.11 m/s, a=9.573 m/s²) | An object starts with initial velocity 26.11 m/s and experiences constant acceleration 9.573 m/s² for 4.145 s. Final velocity: v = v0 + a t = 26.11 + (9.573)(4.145) = 65.79 m/s. Displacement: s = v0 t + (1/2) a t² = 190.4 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. |
3,670 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.52 m/s, a=0.7623 m/s²) | An object starts with initial velocity 22.52 m/s and experiences constant acceleration 0.7623 m/s² for 15.81 s. Final velocity: v = v0 + a t = 22.52 + (0.7623)(15.81) = 34.57 m/s. Displacement: s = v0 t + (1/2) a t² = 451.3 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. |
3,671 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.03 m/s, a=-0.9276 m/s²) | An object starts with initial velocity 12.03 m/s and experiences constant acceleration -0.9276 m/s² for 4.497 s. Final velocity: v = v0 + a t = 12.03 + (-0.9276)(4.497) = 7.854 m/s. Displacement: s = v0 t + (1/2) a t² = 44.7 m. These relations follow directly from the definitions of average velocity and constant accele... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
3,672 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.8 m/s, a=-1.733 m/s²) | An object starts with initial velocity 4.8 m/s and experiences constant acceleration -1.733 m/s² for 14.24 s. Final velocity: v = v0 + a t = 4.8 + (-1.733)(14.24) = -19.87 m/s. Displacement: s = v0 t + (1/2) a t² = -107.3 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. |
3,673 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.37 m/s, a=6.86 m/s²) | An object starts with initial velocity 26.37 m/s and experiences constant acceleration 6.86 m/s² for 9.653 s. Final velocity: v = v0 + a t = 26.37 + (6.86)(9.653) = 92.59 m/s. Displacement: s = v0 t + (1/2) a t² = 574.2 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. |
3,674 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.23 m/s, a=2.876 m/s²) | An object starts with initial velocity 21.23 m/s and experiences constant acceleration 2.876 m/s² for 6.765 s. Final velocity: v = v0 + a t = 21.23 + (2.876)(6.765) = 40.69 m/s. Displacement: s = v0 t + (1/2) a t² = 209.4 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. |
3,675 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.61 m/s, a=5.624 m/s²) | An object starts with initial velocity 6.61 m/s and experiences constant acceleration 5.624 m/s² for 11.49 s. Final velocity: v = v0 + a t = 6.61 + (5.624)(11.49) = 71.23 m/s. Displacement: s = v0 t + (1/2) a t² = 447.2 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. |
3,676 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.133 m/s, a=-4.316 m/s²) | An object starts with initial velocity 5.133 m/s and experiences constant acceleration -4.316 m/s² for 5.526 s. Final velocity: v = v0 + a t = 5.133 + (-4.316)(5.526) = -18.72 m/s. Displacement: s = v0 t + (1/2) a t² = -37.53 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. |
3,677 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.173 m/s, a=-2.778 m/s²) | An object starts with initial velocity 1.173 m/s and experiences constant acceleration -2.778 m/s² for 17.79 s. Final velocity: v = v0 + a t = 1.173 + (-2.778)(17.79) = -48.24 m/s. Displacement: s = v0 t + (1/2) a t² = -418.6 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. |
3,678 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.82 m/s, a=-0.9435 m/s²) | An object starts with initial velocity 27.82 m/s and experiences constant acceleration -0.9435 m/s² for 16.02 s. Final velocity: v = v0 + a t = 27.82 + (-0.9435)(16.02) = 12.7 m/s. Displacement: s = v0 t + (1/2) a t² = 324.6 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. |
3,679 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.27 m/s, a=-1.265 m/s²) | An object starts with initial velocity 19.27 m/s and experiences constant acceleration -1.265 m/s² for 16.64 s. Final velocity: v = v0 + a t = 19.27 + (-1.265)(16.64) = -1.781 m/s. Displacement: s = v0 t + (1/2) a t² = 145.6 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. |
3,680 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 26.96 kg, acceleration 0.1209 m/s² | A net force acting on a mass of 26.96 kg produces an acceleration of 0.1209 m/s². By Newton's second law, F_net = m a = 26.96 × 0.1209 = 3.259 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,681 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 17.7 kg, acceleration 9.117 m/s² | A net force acting on a mass of 17.7 kg produces an acceleration of 9.117 m/s². By Newton's second law, F_net = m a = 17.7 × 9.117 = 161.4 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,682 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 18.77 kg, acceleration 1.34 m/s² | A net force acting on a mass of 18.77 kg produces an acceleration of 1.34 m/s². By Newton's second law, F_net = m a = 18.77 × 1.34 = 25.16 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,683 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 35.42 kg, acceleration 8.284 m/s² | A net force acting on a mass of 35.42 kg produces an acceleration of 8.284 m/s². By Newton's second law, F_net = m a = 35.42 × 8.284 = 293.4 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,684 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 36.24 kg, acceleration 6.184 m/s² | A net force acting on a mass of 36.24 kg produces an acceleration of 6.184 m/s². By Newton's second law, F_net = m a = 36.24 × 6.184 = 224.1 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,685 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 30.77 kg, acceleration 4.937 m/s² | A net force acting on a mass of 30.77 kg produces an acceleration of 4.937 m/s². By Newton's second law, F_net = m a = 30.77 × 4.937 = 151.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,686 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 3.335 kg, acceleration 12.26 m/s² | A net force acting on a mass of 3.335 kg produces an acceleration of 12.26 m/s². By Newton's second law, F_net = m a = 3.335 × 12.26 = 40.87 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,687 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 41.28 kg, acceleration 3.367 m/s² | A net force acting on a mass of 41.28 kg produces an acceleration of 3.367 m/s². By Newton's second law, F_net = m a = 41.28 × 3.367 = 139 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,688 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 48.28 kg, acceleration 2.733 m/s² | A net force acting on a mass of 48.28 kg produces an acceleration of 2.733 m/s². By Newton's second law, F_net = m a = 48.28 × 2.733 = 132 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,689 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 48.59 kg, acceleration 8.107 m/s² | A net force acting on a mass of 48.59 kg produces an acceleration of 8.107 m/s². By Newton's second law, F_net = m a = 48.59 × 8.107 = 394 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,690 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 48.95 kg, acceleration 11.69 m/s² | A net force acting on a mass of 48.95 kg produces an acceleration of 11.69 m/s². By Newton's second law, F_net = m a = 48.95 × 11.69 = 572.5 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,691 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 39.14 kg, acceleration 1.686 m/s² | A net force acting on a mass of 39.14 kg produces an acceleration of 1.686 m/s². By Newton's second law, F_net = m a = 39.14 × 1.686 = 65.98 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,692 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 37.42 kg, acceleration 5.792 m/s² | A net force acting on a mass of 37.42 kg produces an acceleration of 5.792 m/s². By Newton's second law, F_net = m a = 37.42 × 5.792 = 216.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,693 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 32.86 kg, acceleration 13.06 m/s² | A net force acting on a mass of 32.86 kg produces an acceleration of 13.06 m/s². By Newton's second law, F_net = m a = 32.86 × 13.06 = 429.3 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,694 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 31.9 kg, acceleration 8.308 m/s² | A net force acting on a mass of 31.9 kg produces an acceleration of 8.308 m/s². By Newton's second law, F_net = m a = 31.9 × 8.308 = 265 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,695 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 40.93 kg, acceleration 3.388 m/s² | A net force acting on a mass of 40.93 kg produces an acceleration of 3.388 m/s². By Newton's second law, F_net = m a = 40.93 × 3.388 = 138.7 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,696 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 13.81 kg, acceleration 8.767 m/s² | A net force acting on a mass of 13.81 kg produces an acceleration of 8.767 m/s². By Newton's second law, F_net = m a = 13.81 × 8.767 = 121 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,697 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 40.48 kg, acceleration 11.32 m/s² | A net force acting on a mass of 40.48 kg produces an acceleration of 11.32 m/s². By Newton's second law, F_net = m a = 40.48 × 11.32 = 458.2 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,698 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 8.204 kg, acceleration 3.553 m/s² | A net force acting on a mass of 8.204 kg produces an acceleration of 3.553 m/s². By Newton's second law, F_net = m a = 8.204 × 3.553 = 29.15 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,699 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 36.45 kg, acceleration 5.593 m/s² | A net force acting on a mass of 36.45 kg produces an acceleration of 5.593 m/s². By Newton's second law, F_net = m a = 36.45 × 5.593 = 203.9 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
3,700 | physics | mechanics | newton_second_law | 3 | worked_example | Newton's second law: mass 45.16 kg, acceleration 1.496 m/s² | A net force acting on a mass of 45.16 kg produces an acceleration of 1.496 m/s². By Newton's second law, F_net = m a = 45.16 × 1.496 = 67.56 N. Direction of F_net is the same as the direction of the acceleration. This relation defines the inertial mass and is the foundation of classical dynamics. | F_net = m a | kinematics_1d | Compute net force from mass and acceleration using Newton's second law. |
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