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values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
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1,801 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=25.86 m/s, a=-2.193 m/s²) | An object starts with initial velocity 25.86 m/s and experiences constant acceleration -2.193 m/s² for 5.994 s. Final velocity: v = v0 + a t = 25.86 + (-2.193)(5.994) = 12.71 m/s. Displacement: s = v0 t + (1/2) a t² = 115.6 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. |
1,802 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.082 m/s, a=9.378 m/s²) | An object starts with initial velocity 8.082 m/s and experiences constant acceleration 9.378 m/s² for 7.519 s. Final velocity: v = v0 + a t = 8.082 + (9.378)(7.519) = 78.59 m/s. Displacement: s = v0 t + (1/2) a t² = 325.8 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. |
1,803 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.517 m/s, a=1.359 m/s²) | An object starts with initial velocity 5.517 m/s and experiences constant acceleration 1.359 m/s² for 8.963 s. Final velocity: v = v0 + a t = 5.517 + (1.359)(8.963) = 17.7 m/s. Displacement: s = v0 t + (1/2) a t² = 104 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. |
1,804 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.57 m/s, a=0.4762 m/s²) | An object starts with initial velocity 22.57 m/s and experiences constant acceleration 0.4762 m/s² for 8.611 s. Final velocity: v = v0 + a t = 22.57 + (0.4762)(8.611) = 26.67 m/s. Displacement: s = v0 t + (1/2) a t² = 212 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. |
1,805 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.52 m/s, a=3.571 m/s²) | An object starts with initial velocity 13.52 m/s and experiences constant acceleration 3.571 m/s² for 19.61 s. Final velocity: v = v0 + a t = 13.52 + (3.571)(19.61) = 83.54 m/s. Displacement: s = v0 t + (1/2) a t² = 951.5 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. |
1,806 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.58 m/s, a=7.213 m/s²) | An object starts with initial velocity 20.58 m/s and experiences constant acceleration 7.213 m/s² for 14.7 s. Final velocity: v = v0 + a t = 20.58 + (7.213)(14.7) = 126.6 m/s. Displacement: s = v0 t + (1/2) a t² = 1081 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. |
1,807 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.12 m/s, a=3.33 m/s²) | An object starts with initial velocity 24.12 m/s and experiences constant acceleration 3.33 m/s² for 17.27 s. Final velocity: v = v0 + a t = 24.12 + (3.33)(17.27) = 81.63 m/s. Displacement: s = v0 t + (1/2) a t² = 913.2 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. |
1,808 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.882 m/s, a=7.001 m/s²) | An object starts with initial velocity 5.882 m/s and experiences constant acceleration 7.001 m/s² for 15.03 s. Final velocity: v = v0 + a t = 5.882 + (7.001)(15.03) = 111.1 m/s. Displacement: s = v0 t + (1/2) a t² = 879.4 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. |
1,809 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.19 m/s, a=-4.854 m/s²) | An object starts with initial velocity 14.19 m/s and experiences constant acceleration -4.854 m/s² for 9.009 s. Final velocity: v = v0 + a t = 14.19 + (-4.854)(9.009) = -29.54 m/s. Displacement: s = v0 t + (1/2) a t² = -69.14 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. |
1,810 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.034 m/s, a=8.399 m/s²) | An object starts with initial velocity 4.034 m/s and experiences constant acceleration 8.399 m/s² for 12.98 s. Final velocity: v = v0 + a t = 4.034 + (8.399)(12.98) = 113.1 m/s. Displacement: s = v0 t + (1/2) a t² = 760.2 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. |
1,811 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.02 m/s, a=-0.2641 m/s²) | An object starts with initial velocity 16.02 m/s and experiences constant acceleration -0.2641 m/s² for 10.25 s. Final velocity: v = v0 + a t = 16.02 + (-0.2641)(10.25) = 13.31 m/s. Displacement: s = v0 t + (1/2) a t² = 150.3 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. |
1,812 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.529 m/s, a=7.878 m/s²) | An object starts with initial velocity 7.529 m/s and experiences constant acceleration 7.878 m/s² for 1.906 s. Final velocity: v = v0 + a t = 7.529 + (7.878)(1.906) = 22.55 m/s. Displacement: s = v0 t + (1/2) a t² = 28.67 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. |
1,813 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.969 m/s, a=-2.55 m/s²) | An object starts with initial velocity 2.969 m/s and experiences constant acceleration -2.55 m/s² for 5.094 s. Final velocity: v = v0 + a t = 2.969 + (-2.55)(5.094) = -10.02 m/s. Displacement: s = v0 t + (1/2) a t² = -17.96 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. |
1,814 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.629 m/s, a=7.585 m/s²) | An object starts with initial velocity 7.629 m/s and experiences constant acceleration 7.585 m/s² for 2.83 s. Final velocity: v = v0 + a t = 7.629 + (7.585)(2.83) = 29.09 m/s. Displacement: s = v0 t + (1/2) a t² = 51.95 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. |
1,815 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.34 m/s, a=-1.103 m/s²) | An object starts with initial velocity 22.34 m/s and experiences constant acceleration -1.103 m/s² for 7.846 s. Final velocity: v = v0 + a t = 22.34 + (-1.103)(7.846) = 13.68 m/s. Displacement: s = v0 t + (1/2) a t² = 141.3 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. |
1,816 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.72 m/s, a=7.15 m/s²) | An object starts with initial velocity 16.72 m/s and experiences constant acceleration 7.15 m/s² for 7.539 s. Final velocity: v = v0 + a t = 16.72 + (7.15)(7.539) = 70.63 m/s. Displacement: s = v0 t + (1/2) a t² = 329.3 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. |
1,817 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.35 m/s, a=0.2664 m/s²) | An object starts with initial velocity 12.35 m/s and experiences constant acceleration 0.2664 m/s² for 13.91 s. Final velocity: v = v0 + a t = 12.35 + (0.2664)(13.91) = 16.06 m/s. Displacement: s = v0 t + (1/2) a t² = 197.6 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. |
1,818 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.17 m/s, a=3.653 m/s²) | An object starts with initial velocity 18.17 m/s and experiences constant acceleration 3.653 m/s² for 13.35 s. Final velocity: v = v0 + a t = 18.17 + (3.653)(13.35) = 66.92 m/s. Displacement: s = v0 t + (1/2) a t² = 567.9 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. |
1,819 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.15 m/s, a=9.691 m/s²) | An object starts with initial velocity 16.15 m/s and experiences constant acceleration 9.691 m/s² for 6.408 s. Final velocity: v = v0 + a t = 16.15 + (9.691)(6.408) = 78.25 m/s. Displacement: s = v0 t + (1/2) a t² = 302.4 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. |
1,820 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=9.753 m/s, a=2.657 m/s²) | An object starts with initial velocity 9.753 m/s and experiences constant acceleration 2.657 m/s² for 15.72 s. Final velocity: v = v0 + a t = 9.753 + (2.657)(15.72) = 51.52 m/s. Displacement: s = v0 t + (1/2) a t² = 481.6 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. |
1,821 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.41 m/s, a=-3.824 m/s²) | An object starts with initial velocity 13.41 m/s and experiences constant acceleration -3.824 m/s² for 12.66 s. Final velocity: v = v0 + a t = 13.41 + (-3.824)(12.66) = -35 m/s. Displacement: s = v0 t + (1/2) a t² = -136.7 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. |
1,822 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.91 m/s, a=9.349 m/s²) | An object starts with initial velocity 13.91 m/s and experiences constant acceleration 9.349 m/s² for 17.5 s. Final velocity: v = v0 + a t = 13.91 + (9.349)(17.5) = 177.5 m/s. Displacement: s = v0 t + (1/2) a t² = 1674 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. |
1,823 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.22 m/s, a=8.929 m/s²) | An object starts with initial velocity 19.22 m/s and experiences constant acceleration 8.929 m/s² for 9.015 s. Final velocity: v = v0 + a t = 19.22 + (8.929)(9.015) = 99.7 m/s. Displacement: s = v0 t + (1/2) a t² = 536 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. |
1,824 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.37 m/s, a=1.072 m/s²) | An object starts with initial velocity 18.37 m/s and experiences constant acceleration 1.072 m/s² for 18.23 s. Final velocity: v = v0 + a t = 18.37 + (1.072)(18.23) = 37.91 m/s. Displacement: s = v0 t + (1/2) a t² = 513.1 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. |
1,825 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.373 m/s, a=0.1544 m/s²) | An object starts with initial velocity 2.373 m/s and experiences constant acceleration 0.1544 m/s² for 6.956 s. Final velocity: v = v0 + a t = 2.373 + (0.1544)(6.956) = 3.447 m/s. Displacement: s = v0 t + (1/2) a t² = 20.24 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. |
1,826 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.59 m/s, a=5.657 m/s²) | An object starts with initial velocity 19.59 m/s and experiences constant acceleration 5.657 m/s² for 12.5 s. Final velocity: v = v0 + a t = 19.59 + (5.657)(12.5) = 90.31 m/s. Displacement: s = v0 t + (1/2) a t² = 687 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. |
1,827 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.86 m/s, a=8.315 m/s²) | An object starts with initial velocity 11.86 m/s and experiences constant acceleration 8.315 m/s² for 15.84 s. Final velocity: v = v0 + a t = 11.86 + (8.315)(15.84) = 143.6 m/s. Displacement: s = v0 t + (1/2) a t² = 1231 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. |
1,828 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.16 m/s, a=6.218 m/s²) | An object starts with initial velocity 28.16 m/s and experiences constant acceleration 6.218 m/s² for 10.9 s. Final velocity: v = v0 + a t = 28.16 + (6.218)(10.9) = 95.93 m/s. Displacement: s = v0 t + (1/2) a t² = 676.2 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. |
1,829 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.51 m/s, a=-2.49 m/s²) | An object starts with initial velocity 13.51 m/s and experiences constant acceleration -2.49 m/s² for 17.23 s. Final velocity: v = v0 + a t = 13.51 + (-2.49)(17.23) = -29.4 m/s. Displacement: s = v0 t + (1/2) a t² = -136.9 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. |
1,830 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.751 m/s, a=-1.481 m/s²) | An object starts with initial velocity 3.751 m/s and experiences constant acceleration -1.481 m/s² for 5.781 s. Final velocity: v = v0 + a t = 3.751 + (-1.481)(5.781) = -4.809 m/s. Displacement: s = v0 t + (1/2) a t² = -3.056 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. |
1,831 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.32 m/s, a=6.246 m/s²) | An object starts with initial velocity 22.32 m/s and experiences constant acceleration 6.246 m/s² for 5.001 s. Final velocity: v = v0 + a t = 22.32 + (6.246)(5.001) = 53.55 m/s. Displacement: s = v0 t + (1/2) a t² = 189.7 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. |
1,832 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.91 m/s, a=-3.567 m/s²) | An object starts with initial velocity 11.91 m/s and experiences constant acceleration -3.567 m/s² for 18.8 s. Final velocity: v = v0 + a t = 11.91 + (-3.567)(18.8) = -55.14 m/s. Displacement: s = v0 t + (1/2) a t² = -406.3 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. |
1,833 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.2 m/s, a=-4.193 m/s²) | An object starts with initial velocity 14.2 m/s and experiences constant acceleration -4.193 m/s² for 15.65 s. Final velocity: v = v0 + a t = 14.2 + (-4.193)(15.65) = -51.41 m/s. Displacement: s = v0 t + (1/2) a t² = -291.2 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. |
1,834 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.72 m/s, a=9.94 m/s²) | An object starts with initial velocity 15.72 m/s and experiences constant acceleration 9.94 m/s² for 2.975 s. Final velocity: v = v0 + a t = 15.72 + (9.94)(2.975) = 45.29 m/s. Displacement: s = v0 t + (1/2) a t² = 90.74 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. |
1,835 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.54 m/s, a=-3.735 m/s²) | An object starts with initial velocity 18.54 m/s and experiences constant acceleration -3.735 m/s² for 18.7 s. Final velocity: v = v0 + a t = 18.54 + (-3.735)(18.7) = -51.31 m/s. Displacement: s = v0 t + (1/2) a t² = -306.4 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. |
1,836 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.7 m/s, a=-1.56 m/s²) | An object starts with initial velocity 11.7 m/s and experiences constant acceleration -1.56 m/s² for 15.01 s. Final velocity: v = v0 + a t = 11.7 + (-1.56)(15.01) = -11.72 m/s. Displacement: s = v0 t + (1/2) a t² = -0.1982 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. |
1,837 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.29 m/s, a=-3.104 m/s²) | An object starts with initial velocity 13.29 m/s and experiences constant acceleration -3.104 m/s² for 11.01 s. Final velocity: v = v0 + a t = 13.29 + (-3.104)(11.01) = -20.87 m/s. Displacement: s = v0 t + (1/2) a t² = -41.71 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. |
1,838 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.118 m/s, a=-4.473 m/s²) | An object starts with initial velocity 5.118 m/s and experiences constant acceleration -4.473 m/s² for 7.78 s. Final velocity: v = v0 + a t = 5.118 + (-4.473)(7.78) = -29.68 m/s. Displacement: s = v0 t + (1/2) a t² = -95.54 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. |
1,839 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=27.46 m/s, a=7.964 m/s²) | An object starts with initial velocity 27.46 m/s and experiences constant acceleration 7.964 m/s² for 9.877 s. Final velocity: v = v0 + a t = 27.46 + (7.964)(9.877) = 106.1 m/s. Displacement: s = v0 t + (1/2) a t² = 659.6 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. |
1,840 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.13 m/s, a=9.023 m/s²) | An object starts with initial velocity 26.13 m/s and experiences constant acceleration 9.023 m/s² for 11.42 s. Final velocity: v = v0 + a t = 26.13 + (9.023)(11.42) = 129.2 m/s. Displacement: s = v0 t + (1/2) a t² = 887 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. |
1,841 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.053 m/s, a=9.227 m/s²) | An object starts with initial velocity 4.053 m/s and experiences constant acceleration 9.227 m/s² for 11.25 s. Final velocity: v = v0 + a t = 4.053 + (9.227)(11.25) = 107.8 m/s. Displacement: s = v0 t + (1/2) a t² = 629.1 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. |
1,842 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=17.72 m/s, a=1.848 m/s²) | An object starts with initial velocity 17.72 m/s and experiences constant acceleration 1.848 m/s² for 15.23 s. Final velocity: v = v0 + a t = 17.72 + (1.848)(15.23) = 45.87 m/s. Displacement: s = v0 t + (1/2) a t² = 484.3 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. |
1,843 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.32 m/s, a=1.525 m/s²) | An object starts with initial velocity 26.32 m/s and experiences constant acceleration 1.525 m/s² for 13.16 s. Final velocity: v = v0 + a t = 26.32 + (1.525)(13.16) = 46.38 m/s. Displacement: s = v0 t + (1/2) a t² = 478.2 m. These relations follow directly from the definitions of average velocity and constant 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. |
1,844 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.01 m/s, a=8.634 m/s²) | An object starts with initial velocity 16.01 m/s and experiences constant acceleration 8.634 m/s² for 10.15 s. Final velocity: v = v0 + a t = 16.01 + (8.634)(10.15) = 103.7 m/s. Displacement: s = v0 t + (1/2) a t² = 607.4 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. |
1,845 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.814 m/s, a=-3.657 m/s²) | An object starts with initial velocity 6.814 m/s and experiences constant acceleration -3.657 m/s² for 6.849 s. Final velocity: v = v0 + a t = 6.814 + (-3.657)(6.849) = -18.23 m/s. Displacement: s = v0 t + (1/2) a t² = -39.11 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. |
1,846 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=12.37 m/s, a=-2.664 m/s²) | An object starts with initial velocity 12.37 m/s and experiences constant acceleration -2.664 m/s² for 1.201 s. Final velocity: v = v0 + a t = 12.37 + (-2.664)(1.201) = 9.168 m/s. Displacement: s = v0 t + (1/2) a t² = 12.93 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. |
1,847 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.7 m/s, a=6.374 m/s²) | An object starts with initial velocity 15.7 m/s and experiences constant acceleration 6.374 m/s² for 3.59 s. Final velocity: v = v0 + a t = 15.7 + (6.374)(3.59) = 38.58 m/s. Displacement: s = v0 t + (1/2) a t² = 97.43 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. |
1,848 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.603 m/s, a=3.026 m/s²) | An object starts with initial velocity 8.603 m/s and experiences constant acceleration 3.026 m/s² for 14.07 s. Final velocity: v = v0 + a t = 8.603 + (3.026)(14.07) = 51.18 m/s. Displacement: s = v0 t + (1/2) a t² = 420.5 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. |
1,849 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.76 m/s, a=6.332 m/s²) | An object starts with initial velocity 14.76 m/s and experiences constant acceleration 6.332 m/s² for 6.693 s. Final velocity: v = v0 + a t = 14.76 + (6.332)(6.693) = 57.14 m/s. Displacement: s = v0 t + (1/2) a t² = 240.6 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. |
1,850 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=22.98 m/s, a=6.969 m/s²) | An object starts with initial velocity 22.98 m/s and experiences constant acceleration 6.969 m/s² for 12.34 s. Final velocity: v = v0 + a t = 22.98 + (6.969)(12.34) = 109 m/s. Displacement: s = v0 t + (1/2) a t² = 814.5 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. |
1,851 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.9 m/s, a=3.223 m/s²) | An object starts with initial velocity 23.9 m/s and experiences constant acceleration 3.223 m/s² for 4.583 s. Final velocity: v = v0 + a t = 23.9 + (3.223)(4.583) = 38.67 m/s. Displacement: s = v0 t + (1/2) a t² = 143.4 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. |
1,852 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.46 m/s, a=1.557 m/s²) | An object starts with initial velocity 26.46 m/s and experiences constant acceleration 1.557 m/s² for 5.748 s. Final velocity: v = v0 + a t = 26.46 + (1.557)(5.748) = 35.41 m/s. Displacement: s = v0 t + (1/2) a t² = 177.8 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. |
1,853 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.45 m/s, a=4.69 m/s²) | An object starts with initial velocity 21.45 m/s and experiences constant acceleration 4.69 m/s² for 16.74 s. Final velocity: v = v0 + a t = 21.45 + (4.69)(16.74) = 99.96 m/s. Displacement: s = v0 t + (1/2) a t² = 1016 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. |
1,854 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.618 m/s, a=-3.812 m/s²) | An object starts with initial velocity 6.618 m/s and experiences constant acceleration -3.812 m/s² for 12.88 s. Final velocity: v = v0 + a t = 6.618 + (-3.812)(12.88) = -42.48 m/s. Displacement: s = v0 t + (1/2) a t² = -231 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. |
1,855 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.5 m/s, a=6.999 m/s²) | An object starts with initial velocity 15.5 m/s and experiences constant acceleration 6.999 m/s² for 12.65 s. Final velocity: v = v0 + a t = 15.5 + (6.999)(12.65) = 104 m/s. Displacement: s = v0 t + (1/2) a t² = 756.2 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. |
1,856 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.82 m/s, a=-0.922 m/s²) | An object starts with initial velocity 20.82 m/s and experiences constant acceleration -0.922 m/s² for 13.32 s. Final velocity: v = v0 + a t = 20.82 + (-0.922)(13.32) = 8.536 m/s. Displacement: s = v0 t + (1/2) a t² = 195.5 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. |
1,857 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15.96 m/s, a=-0.9677 m/s²) | An object starts with initial velocity 15.96 m/s and experiences constant acceleration -0.9677 m/s² for 4.572 s. Final velocity: v = v0 + a t = 15.96 + (-0.9677)(4.572) = 11.53 m/s. Displacement: s = v0 t + (1/2) a t² = 62.85 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. |
1,858 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=2.054 m/s, a=-2.951 m/s²) | An object starts with initial velocity 2.054 m/s and experiences constant acceleration -2.951 m/s² for 3.097 s. Final velocity: v = v0 + a t = 2.054 + (-2.951)(3.097) = -7.084 m/s. Displacement: s = v0 t + (1/2) a t² = -7.788 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. |
1,859 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=13.66 m/s, a=1.792 m/s²) | An object starts with initial velocity 13.66 m/s and experiences constant acceleration 1.792 m/s² for 14.31 s. Final velocity: v = v0 + a t = 13.66 + (1.792)(14.31) = 39.29 m/s. Displacement: s = v0 t + (1/2) a t² = 378.9 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. |
1,860 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.76 m/s, a=-0.1903 m/s²) | An object starts with initial velocity 14.76 m/s and experiences constant acceleration -0.1903 m/s² for 3.891 s. Final velocity: v = v0 + a t = 14.76 + (-0.1903)(3.891) = 14.02 m/s. Displacement: s = v0 t + (1/2) a t² = 55.99 m. These relations follow directly from the definitions of average velocity and constant 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. |
1,861 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.09 m/s, a=-4.668 m/s²) | An object starts with initial velocity 29.09 m/s and experiences constant acceleration -4.668 m/s² for 19.47 s. Final velocity: v = v0 + a t = 29.09 + (-4.668)(19.47) = -61.82 m/s. Displacement: s = v0 t + (1/2) a t² = -318.6 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. |
1,862 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=8.463 m/s, a=-3.124 m/s²) | An object starts with initial velocity 8.463 m/s and experiences constant acceleration -3.124 m/s² for 9.33 s. Final velocity: v = v0 + a t = 8.463 + (-3.124)(9.33) = -20.69 m/s. Displacement: s = v0 t + (1/2) a t² = -57.02 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. |
1,863 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.2461 m/s, a=-3.647 m/s²) | An object starts with initial velocity 0.2461 m/s and experiences constant acceleration -3.647 m/s² for 1.28 s. Final velocity: v = v0 + a t = 0.2461 + (-3.647)(1.28) = -4.421 m/s. Displacement: s = v0 t + (1/2) a t² = -2.672 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. |
1,864 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=6.516 m/s, a=1.304 m/s²) | An object starts with initial velocity 6.516 m/s and experiences constant acceleration 1.304 m/s² for 15.93 s. Final velocity: v = v0 + a t = 6.516 + (1.304)(15.93) = 27.28 m/s. Displacement: s = v0 t + (1/2) a t² = 269.2 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. |
1,865 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=14.95 m/s, a=0.571 m/s²) | An object starts with initial velocity 14.95 m/s and experiences constant acceleration 0.571 m/s² for 14.24 s. Final velocity: v = v0 + a t = 14.95 + (0.571)(14.24) = 23.08 m/s. Displacement: s = v0 t + (1/2) a t² = 270.8 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. |
1,866 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.9521 m/s, a=-3.797 m/s²) | An object starts with initial velocity 0.9521 m/s and experiences constant acceleration -3.797 m/s² for 15.26 s. Final velocity: v = v0 + a t = 0.9521 + (-3.797)(15.26) = -56.99 m/s. Displacement: s = v0 t + (1/2) a t² = -427.6 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. |
1,867 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.383 m/s, a=-1.002 m/s²) | An object starts with initial velocity 4.383 m/s and experiences constant acceleration -1.002 m/s² for 8.456 s. Final velocity: v = v0 + a t = 4.383 + (-1.002)(8.456) = -4.094 m/s. Displacement: s = v0 t + (1/2) a t² = 1.22 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. |
1,868 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.3 m/s, a=-2.276 m/s²) | An object starts with initial velocity 16.3 m/s and experiences constant acceleration -2.276 m/s² for 18.02 s. Final velocity: v = v0 + a t = 16.3 + (-2.276)(18.02) = -24.71 m/s. Displacement: s = v0 t + (1/2) a t² = -75.83 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. |
1,869 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=7.502 m/s, a=0.7237 m/s²) | An object starts with initial velocity 7.502 m/s and experiences constant acceleration 0.7237 m/s² for 1.24 s. Final velocity: v = v0 + a t = 7.502 + (0.7237)(1.24) = 8.4 m/s. Displacement: s = v0 t + (1/2) a t² = 9.857 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. |
1,870 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.24 m/s, a=5.72 m/s²) | An object starts with initial velocity 29.24 m/s and experiences constant acceleration 5.72 m/s² for 8.311 s. Final velocity: v = v0 + a t = 29.24 + (5.72)(8.311) = 76.78 m/s. Displacement: s = v0 t + (1/2) a t² = 440.6 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. |
1,871 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.25 m/s, a=-1.293 m/s²) | An object starts with initial velocity 29.25 m/s and experiences constant acceleration -1.293 m/s² for 19.9 s. Final velocity: v = v0 + a t = 29.25 + (-1.293)(19.9) = 3.532 m/s. Displacement: s = v0 t + (1/2) a t² = 326.1 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. |
1,872 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=5.975 m/s, a=6.03 m/s²) | An object starts with initial velocity 5.975 m/s and experiences constant acceleration 6.03 m/s² for 2.785 s. Final velocity: v = v0 + a t = 5.975 + (6.03)(2.785) = 22.77 m/s. Displacement: s = v0 t + (1/2) a t² = 40.03 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. |
1,873 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=19.98 m/s, a=-1.873 m/s²) | An object starts with initial velocity 19.98 m/s and experiences constant acceleration -1.873 m/s² for 8.393 s. Final velocity: v = v0 + a t = 19.98 + (-1.873)(8.393) = 4.257 m/s. Displacement: s = v0 t + (1/2) a t² = 101.7 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. |
1,874 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=28.84 m/s, a=9.043 m/s²) | An object starts with initial velocity 28.84 m/s and experiences constant acceleration 9.043 m/s² for 4.014 s. Final velocity: v = v0 + a t = 28.84 + (9.043)(4.014) = 65.13 m/s. Displacement: s = v0 t + (1/2) a t² = 188.6 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. |
1,875 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=21.85 m/s, a=6.171 m/s²) | An object starts with initial velocity 21.85 m/s and experiences constant acceleration 6.171 m/s² for 11.44 s. Final velocity: v = v0 + a t = 21.85 + (6.171)(11.44) = 92.45 m/s. Displacement: s = v0 t + (1/2) a t² = 653.9 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. |
1,876 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.664 m/s, a=2.218 m/s²) | An object starts with initial velocity 3.664 m/s and experiences constant acceleration 2.218 m/s² for 6.677 s. Final velocity: v = v0 + a t = 3.664 + (2.218)(6.677) = 18.48 m/s. Displacement: s = v0 t + (1/2) a t² = 73.93 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. |
1,877 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.81 m/s, a=-4.219 m/s²) | An object starts with initial velocity 10.81 m/s and experiences constant acceleration -4.219 m/s² for 13.67 s. Final velocity: v = v0 + a t = 10.81 + (-4.219)(13.67) = -46.84 m/s. Displacement: s = v0 t + (1/2) a t² = -246.2 m. These relations follow directly from the definitions of average velocity and constant accel... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
1,878 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.2 m/s, a=-1.461 m/s²) | An object starts with initial velocity 29.2 m/s and experiences constant acceleration -1.461 m/s² for 9.249 s. Final velocity: v = v0 + a t = 29.2 + (-1.461)(9.249) = 15.69 m/s. Displacement: s = v0 t + (1/2) a t² = 207.6 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. |
1,879 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=0.452 m/s, a=6.916 m/s²) | An object starts with initial velocity 0.452 m/s and experiences constant acceleration 6.916 m/s² for 12.11 s. Final velocity: v = v0 + a t = 0.452 + (6.916)(12.11) = 84.2 m/s. Displacement: s = v0 t + (1/2) a t² = 512.5 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. |
1,880 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.87 m/s, a=-1.354 m/s²) | An object starts with initial velocity 11.87 m/s and experiences constant acceleration -1.354 m/s² for 19.41 s. Final velocity: v = v0 + a t = 11.87 + (-1.354)(19.41) = -14.4 m/s. Displacement: s = v0 t + (1/2) a t² = -24.48 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. |
1,881 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=17.43 m/s, a=5.361 m/s²) | An object starts with initial velocity 17.43 m/s and experiences constant acceleration 5.361 m/s² for 14.08 s. Final velocity: v = v0 + a t = 17.43 + (5.361)(14.08) = 92.92 m/s. Displacement: s = v0 t + (1/2) a t² = 776.8 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. |
1,882 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.65 m/s, a=6.562 m/s²) | An object starts with initial velocity 4.65 m/s and experiences constant acceleration 6.562 m/s² for 5.726 s. Final velocity: v = v0 + a t = 4.65 + (6.562)(5.726) = 42.22 m/s. Displacement: s = v0 t + (1/2) a t² = 134.2 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. |
1,883 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=15 m/s, a=5.289 m/s²) | An object starts with initial velocity 15 m/s and experiences constant acceleration 5.289 m/s² for 7.43 s. Final velocity: v = v0 + a t = 15 + (5.289)(7.43) = 54.3 m/s. Displacement: s = v0 t + (1/2) a t² = 257.4 m. These relations follow directly from the definitions of average velocity and constant acceleration. | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
1,884 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.09 m/s, a=6.393 m/s²) | An object starts with initial velocity 29.09 m/s and experiences constant acceleration 6.393 m/s² for 2.141 s. Final velocity: v = v0 + a t = 29.09 + (6.393)(2.141) = 42.78 m/s. Displacement: s = v0 t + (1/2) a t² = 76.93 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. |
1,885 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=10.67 m/s, a=-2.691 m/s²) | An object starts with initial velocity 10.67 m/s and experiences constant acceleration -2.691 m/s² for 11.19 s. Final velocity: v = v0 + a t = 10.67 + (-2.691)(11.19) = -19.45 m/s. Displacement: s = v0 t + (1/2) a t² = -49.16 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. |
1,886 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=3.222 m/s, a=2.318 m/s²) | An object starts with initial velocity 3.222 m/s and experiences constant acceleration 2.318 m/s² for 7.018 s. Final velocity: v = v0 + a t = 3.222 + (2.318)(7.018) = 19.49 m/s. Displacement: s = v0 t + (1/2) a t² = 79.69 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. |
1,887 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.75 m/s, a=4.67 m/s²) | An object starts with initial velocity 16.75 m/s and experiences constant acceleration 4.67 m/s² for 7.599 s. Final velocity: v = v0 + a t = 16.75 + (4.67)(7.599) = 52.24 m/s. Displacement: s = v0 t + (1/2) a t² = 262.1 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. |
1,888 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.75 m/s, a=5.998 m/s²) | An object starts with initial velocity 26.75 m/s and experiences constant acceleration 5.998 m/s² for 1.406 s. Final velocity: v = v0 + a t = 26.75 + (5.998)(1.406) = 35.19 m/s. Displacement: s = v0 t + (1/2) a t² = 43.53 m. These relations follow directly from the definitions of average velocity and constant 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. |
1,889 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=11.33 m/s, a=5.866 m/s²) | An object starts with initial velocity 11.33 m/s and experiences constant acceleration 5.866 m/s² for 5.763 s. Final velocity: v = v0 + a t = 11.33 + (5.866)(5.763) = 45.14 m/s. Displacement: s = v0 t + (1/2) a t² = 162.7 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. |
1,890 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=1.185 m/s, a=5.599 m/s²) | An object starts with initial velocity 1.185 m/s and experiences constant acceleration 5.599 m/s² for 11.62 s. Final velocity: v = v0 + a t = 1.185 + (5.599)(11.62) = 66.26 m/s. Displacement: s = v0 t + (1/2) a t² = 391.9 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. |
1,891 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.28 m/s, a=2.351 m/s²) | An object starts with initial velocity 16.28 m/s and experiences constant acceleration 2.351 m/s² for 11.77 s. Final velocity: v = v0 + a t = 16.28 + (2.351)(11.77) = 43.95 m/s. Displacement: s = v0 t + (1/2) a t² = 354.4 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. |
1,892 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=16.31 m/s, a=-0.1448 m/s²) | An object starts with initial velocity 16.31 m/s and experiences constant acceleration -0.1448 m/s² for 9.899 s. Final velocity: v = v0 + a t = 16.31 + (-0.1448)(9.899) = 14.88 m/s. Displacement: s = v0 t + (1/2) a t² = 154.4 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. |
1,893 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.03 m/s, a=3.98 m/s²) | An object starts with initial velocity 26.03 m/s and experiences constant acceleration 3.98 m/s² for 17.35 s. Final velocity: v = v0 + a t = 26.03 + (3.98)(17.35) = 95.09 m/s. Displacement: s = v0 t + (1/2) a t² = 1051 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. |
1,894 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=4.81 m/s, a=2.967 m/s²) | An object starts with initial velocity 4.81 m/s and experiences constant acceleration 2.967 m/s² for 9.538 s. Final velocity: v = v0 + a t = 4.81 + (2.967)(9.538) = 33.11 m/s. Displacement: s = v0 t + (1/2) a t² = 180.9 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. |
1,895 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=24.58 m/s, a=3.124 m/s²) | An object starts with initial velocity 24.58 m/s and experiences constant acceleration 3.124 m/s² for 9.628 s. Final velocity: v = v0 + a t = 24.58 + (3.124)(9.628) = 54.66 m/s. Displacement: s = v0 t + (1/2) a t² = 381.5 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. |
1,896 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=23.28 m/s, a=2.589 m/s²) | An object starts with initial velocity 23.28 m/s and experiences constant acceleration 2.589 m/s² for 14.94 s. Final velocity: v = v0 + a t = 23.28 + (2.589)(14.94) = 61.96 m/s. Displacement: s = v0 t + (1/2) a t² = 636.7 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. |
1,897 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=26.49 m/s, a=4.296 m/s²) | An object starts with initial velocity 26.49 m/s and experiences constant acceleration 4.296 m/s² for 7.917 s. Final velocity: v = v0 + a t = 26.49 + (4.296)(7.917) = 60.5 m/s. Displacement: s = v0 t + (1/2) a t² = 344.4 m. These relations follow directly from the definitions of average velocity and constant accelerati... | v = v_0 + a t; s = v_0 t + (1/2) a t^2; v^2 = v_0^2 + 2 a s | definition of velocity and acceleration | Apply the three kinematic equations for constant acceleration in one dimension. |
1,898 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=18.61 m/s, a=-0.1896 m/s²) | An object starts with initial velocity 18.61 m/s and experiences constant acceleration -0.1896 m/s² for 2.203 s. Final velocity: v = v0 + a t = 18.61 + (-0.1896)(2.203) = 18.19 m/s. Displacement: s = v0 t + (1/2) a t² = 40.54 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. |
1,899 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=29.01 m/s, a=7.286 m/s²) | An object starts with initial velocity 29.01 m/s and experiences constant acceleration 7.286 m/s² for 4.608 s. Final velocity: v = v0 + a t = 29.01 + (7.286)(4.608) = 62.58 m/s. Displacement: s = v0 t + (1/2) a t² = 211 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. |
1,900 | physics | mechanics | kinematics_1d | 2 | worked_example | One-dimensional motion with constant acceleration (v0=20.5 m/s, a=6.486 m/s²) | An object starts with initial velocity 20.5 m/s and experiences constant acceleration 6.486 m/s² for 3.928 s. Final velocity: v = v0 + a t = 20.5 + (6.486)(3.928) = 45.98 m/s. Displacement: s = v0 t + (1/2) a t² = 130.6 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. |
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