Representing Motion - AP Physics C Mechanics

1. What is the unit for angular velocity?

   Radians per second (rad/s). Standard unit for rotational velocity.

2. Identify the SI unit for velocity.

   Meters per second (m/s). Standard unit in the International System.

3. State Newton's first law of motion.

   An object in motion stays in motion unless acted upon by a force. Objects maintain constant velocity without net force.

4. What is the formula for velocity in terms of initial velocity, acceleration, and displacement?

   $v_f^2 = v_i^2 + 2as$. Kinematic equation without time variable.

5. What is the period of a circular motion with frequency $f = 2 \text{ Hz}$?

   $T = 0.5 \text{ s}$. Period equals reciprocal of frequency: $T = \frac{1}{f}$.

6. State the formula for instantaneous acceleration.

   $a = \frac{dv}{dt}$. Derivative of velocity with respect to time.

7. What is the acceleration if $v_i = 0$, $v_f = 20 \text{ m/s}$, $t = 4 \text{ s}$.

   $a = 5 \text{ m/s}^2$. Using $a = \frac{v_f - v_i}{t} = \frac{20 - 0}{4} = 5$.

8. Calculate the distance traveled with $v_i = 3 \text{ m/s}$, $a = 2 \text{ m/s}^2$, $t = 5 \text{ s}$.

   $s = 40 \text{ m}$. Using $s = v_i t + \frac{1}{2}at^2 = 3(5) + \frac{1}{2}(2)(25) = 40$.

9. What is the linear velocity if $r = 2 \text{ m}$ and $\omega = 3 \text{ rad/s}$.

   $v = 6 \text{ m/s}$. Using $v = r\omega = 2 \times 3 = 6$.

10. Identify the SI unit for acceleration.

    Meters per second squared (m/s²). Standard unit for rate of velocity change.

11. State the formula for centripetal acceleration.

    $a_c = \frac{v^2}{r}$. Acceleration toward the center of circular path.

12. Find the time taken for $\Delta x = 100 \text{ m}$, $v_{avg} = 5 \text{ m/s}$.

    $\Delta t = 20 \text{ s}$. Rearranging $v_{avg} = \frac{\Delta x}{\Delta t}$ to solve for time.

13. Calculate the angular velocity for $\Delta \theta = 2\pi \text{ rad}$, $\Delta t = 4 \text{ s}$.

    $\omega = \frac{\pi}{2} \text{ rad/s}$. Using $\omega = \frac{\Delta \theta}{\Delta t} = \frac{2\pi}{4} = \frac{\pi}{2}$.

14. What is the displacement if $v_i = 0$, $a = 9.8 \text{ m/s}^2$, $t = 5 \text{ s}$.

    $s = 122.5 \text{ m}$. Using $s = \frac{1}{2}at^2 = \frac{1}{2}(9.8)(25) = 122.5$.

15. What is the formula for average acceleration?

    $a_{avg} = \frac{\Delta v}{\Delta t}$. Change in velocity divided by change in time.

16. Identify the term: The rate of change of velocity.

    Acceleration. Rate of change of velocity.

17. Calculate the final velocity of an object with $v_i = 0$, $a = 9.8 \text{ m/s}^2$, $t = 3 \text{ s}$.

    $v_f = 29.4 \text{ m/s}$. Using $v_f = v_i + at = 0 + 9.8(3) = 29.4$.

18. What is the definition of displacement?

    Displacement is the change in position. Vector from initial to final position.

19. Determine the centripetal acceleration for $v = 10 \text{ m/s}$, $r = 5 \text{ m}$.

    $a_c = 20 \text{ m/s}^2$. Using $a_c = \frac{v^2}{r} = \frac{100}{5} = 20$.

20. What is the formula for angular velocity?

    $\omega = \frac{\Delta \theta}{\Delta t}$. Rate of change of angular position.

21. What is the term for motion under the influence of gravity alone?

    Free fall. Motion with only gravitational force acting.

22. Determine the linear velocity if $r = 0.5 \text{ m}$ and $\omega = 4 \text{ rad/s}$.

    $v = 2 \text{ m/s}$. Using $v = r\omega = 0.5 \times 4 = 2$.

23. State the definition of period in circular motion.

    The time for one complete revolution. Time for object to complete one full cycle.

24. Calculate the displacement given $v_i = 2 \text{ m/s}$, $a = 3 \text{ m/s}^2$, $t = 4 \text{ s}$.

    $s = 28 \text{ m}$. Using $s = v_i t + \frac{1}{2}at^2 = 2(4) + \frac{1}{2}(3)(16) = 28$.

25. What is the formula for average velocity?

    $v_{avg} = \frac{\Delta x}{\Delta t}$. Change in position divided by change in time.

26. Determine the time for $v_i = 0$, $a = 9.8 \text{ m/s}^2$, $v_f = 49 \text{ m/s}$.

    $t = 5 \text{ s}$. Using $t = \frac{v_f - v_i}{a} = \frac{49 - 0}{9.8} = 5$.

27. Identify the formula that relates linear and angular velocity.

    $v = r\omega$. Linear speed equals radius times angular velocity.

28. Determine the distance fallen for $t = 3 \text{ s}$ under gravity $g = 9.8 \text{ m/s}^2$.

    $s = 44.1 \text{ m}$. Using $s = \frac{1}{2}gt^2 = \frac{1}{2}(9.8)(9) = 44.1$.

29. State the equation for final velocity in uniformly accelerated motion.

    $v_f = v_i + at$. Kinematic equation for constant acceleration.

30. What is the equation for displacement in uniformly accelerated motion?

    $s = v_i t + \frac{1}{2} a t^2$. Position equation for constant acceleration motion.

31. Calculate the average acceleration for $\Delta v = 15 \text{ m/s}$, $\Delta t = 3 \text{ s}$.

    $a_{avg} = 5 \text{ m/s}^2$. Change in velocity divided by time interval.

32. Find the final velocity for $v_i = 15 \text{ m/s}$, $a = 4 \text{ m/s}^2$, $t = 5 \text{ s}$.

    $v_f = 35 \text{ m/s}$. Using $v_f = v_i + at = 15 + 4(5) = 35$.

33. Find the average velocity for a trip with $\Delta x = 50 \text{ m}$ and $\Delta t = 10 \text{ s}$.

    $v_{avg} = 5 \text{ m/s}$. Total displacement divided by total time.

34. Find the displacement for $v_i = 5 \text{ m/s}$, $v_f = 25 \text{ m/s}$, $t = 4 \text{ s}$.

    $s = 60 \text{ m}$. Using average velocity: $s = \frac{v_i + v_f}{2} \times t = 15 \times 4 = 60$.

35. Find the initial velocity if $v_f = 30 \text{ m/s}$, $a = 10 \text{ m/s}^2$, $t = 2 \text{ s}$.

    $v_i = 10 \text{ m/s}$. Rearranging $v_f = v_i + at$ to solve for $v_i$.

36. State the formula for instantaneous velocity.

    $v = \frac{dx}{dt}$. Derivative of position with respect to time.

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