Displacement, Velocity, and Acceleration - AP Physics 1

1. Find the acceleration given $v_i = 5 \text{ m/s}$, $v_f = 15 \text{ m/s}$, and $t = 2 \text{ s}$.

   $a = 5 \text{ m/s}^2$. Using $a = \frac{\Delta v}{t} = \frac{10}{2}$.

2. What does a horizontal line on a velocity-time graph indicate?

   Constant velocity. Zero acceleration means no change in velocity.

3. If velocity and acceleration have the same sign, what happens to speed?

   Speed increases. Same direction means acceleration adds to speed.

4. Find the average acceleration given $\text{change in velocity} = 10 \text{ m/s}$ and $t = 5 \text{ s}$.

   $a_{avg} = 2 \text{ m/s}^2$. Using $a_{avg} = \frac{\Delta v}{t} = \frac{10}{5}$.

5. What is the acceleration due to gravity near Earth's surface?

   $9.8 \text{ m/s}^2$. Standard acceleration due to Earth's gravity.

6. What is the formula for final velocity squared in uniformly accelerated motion?

   $v_f^2 = v_i^2 + 2as$. Kinematic equation relating velocities and displacement.

7. Find the displacement for $v_i = 10 \text{ m/s}$, $a = 0$, and $t = 3 \text{ s}$.

   $s = 30 \text{ m}$. Using $s = v_i t = 10(3)$ with no acceleration.

8. What is the formula for displacement in terms of initial and final position?

   $s = x_f - x_i$. Change in position from initial to final location.

9. If a car decelerates, what is the sign of its acceleration relative to velocity?

   Opposite sign. Deceleration means acceleration opposes velocity direction.

10. Find the average velocity given $s = 20 \text{ m}$ and $t = 4 \text{ s}$.

    $v_{avg} = 5 \text{ m/s}$. Using $v_{avg} = \frac{s}{t} = \frac{20}{4}$.

11. What is the formula for final velocity in uniformly accelerated motion?

    $v_f = v_i + at$. Initial velocity plus acceleration times time.

12. Identify the SI unit of displacement.

    Meter (m). Standard unit for distance and position in physics.

13. Identify the SI unit of velocity.

    Meter per second (m/s). Standard unit for rate of change of position.

14. What is the instantaneous velocity at the peak of a projectile's trajectory?

    $0 \text{ m/s}$ (Vertical component). Only vertical component is zero at maximum height.

15. What does a negative value for displacement indicate?

    Movement in the opposite direction. Negative indicates direction opposite to reference.

16. What happens to the velocity when acceleration is zero?

    Velocity remains constant. Zero rate of change means constant value.

17. What is the effect on velocity if acceleration is opposite to velocity?

    Velocity decreases. Opposing acceleration causes deceleration.

18. What is the formula for average acceleration?

    $a_{avg} = \frac{\text{change in velocity}}{\text{time}}$. Change in velocity divided by time interval.

19. State the formula for average velocity.

    $v_{avg} = \frac{\text{displacement}}{\text{time}}$. Displacement divided by time interval.

20. Which physical quantity is described by the slope of a velocity-time graph?

    Acceleration. Rate of change of velocity with respect to time.

21. State the formula for instantaneous velocity.

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

22. What does a flat line on a position-time graph indicate?

    No movement. Zero slope indicates constant position.

23. Identify the SI unit of acceleration.

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

24. What is the result of integrating acceleration with respect to time?

    Velocity. Integration of acceleration yields velocity.

25. What is the formula for displacement with uniform acceleration?

    $s = v_i t + \frac{1}{2}at^2$. Kinematic equation for position with constant acceleration.

26. What does zero acceleration indicate about velocity?

    Velocity is constant. Zero rate of change means no velocity change.

27. Find the displacement when $v_i = 0$, $a = 2 \text{ m/s}^2$, and $t = 3 \text{ s}$.

    $s = 9 \text{ m}$. Using $s = \frac{1}{2}at^2 = \frac{1}{2}(2)(3^2)$.

28. Find the final velocity when $v_i = 0$, $a = 4 \text{ m/s}^2$, and $t = 2 \text{ s}$.

    $v_f = 8 \text{ m/s}$. Using $v_f = v_i + at = 0 + 4(2)$.

29. Which physical quantity is described by the slope of a position-time graph?

    Velocity. Rate of change of position with respect to time.

30. Describe the velocity-time graph for an object with constant acceleration.

    Straight line with a slope. Constant acceleration produces linear velocity graph.

31. If velocity is zero, what can be said about displacement?

    Displacement may be zero or non-zero. Zero velocity doesn't determine displacement value.

32. State the formula for instantaneous acceleration.

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

33. Describe the motion when acceleration is zero.

    Constant velocity. Zero acceleration means velocity doesn't change.

34. How does velocity change when acceleration is constant and non-zero?

    Linearly. Constant acceleration produces linear velocity change.

35. If an object is thrown upwards, what is its acceleration at the highest point?

    $9.8 \text{ m/s}^2$ downward. Gravity acts continuously downward throughout flight.

36. What is the relationship between initial velocity and displacement when acceleration is zero?

    Directly proportional. With zero acceleration, $s = v_i t$.

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