AP Physics Questions on Displacement, Velocity, and Acceleration

📚 Quick Study Guide

• 📏 Displacement: The change in position of an object. It's a vector quantity, meaning it has both magnitude and direction. Formula: $\Delta x = x_f - x_i$, where $x_f$ is the final position and $x_i$ is the initial position.
• ⏱️ Velocity: The rate of change of displacement with respect to time. Average velocity: $\bar{v} = \frac{\Delta x}{\Delta t}$. Instantaneous velocity: $v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$.
• 📈 Acceleration: The rate of change of velocity with respect to time. Average acceleration: $\bar{a} = \frac{\Delta v}{\Delta t}$. Instantaneous acceleration: $a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t}$.
• 🍎 Constant Acceleration Equations (Kinematics): These equations apply when acceleration is constant:
  • $v = v_0 + at$
  • $\Delta x = v_0t + \frac{1}{2}at^2$
  • $v^2 = v_0^2 + 2a\Delta x$
  • $\Delta x = \frac{1}{2}(v + v_0)t$
• 🧭 Vector vs. Scalar: Displacement, velocity, and acceleration are vector quantities (magnitude and direction). Distance and speed are scalar quantities (magnitude only).

🧪 Practice Quiz

1. A car travels 20 meters east, then 30 meters north. What is the magnitude of the car's total displacement?
   1. 10 m
   2. 50 m
   3. 36 m
   4. 25 m
2. An object moves with a constant velocity of 5 m/s east. What is its acceleration?
   1. 5 m/s² east
   2. 5 m/s² west
   3. 0 m/s²
   4. 10 m/s² east
3. A ball is thrown vertically upwards with an initial velocity of 10 m/s. Assuming acceleration due to gravity is -9.8 m/s², what is the ball's velocity at its highest point?
   1. 10 m/s
   2. -10 m/s
   3. 9.8 m/s
   4. 0 m/s
4. A car accelerates from rest to 20 m/s in 5 seconds. What is the car's average acceleration?
   1. 2 m/s²
   2. 4 m/s²
   3. 5 m/s²
   4. 10 m/s²
5. A runner completes one lap around a 400-meter track in 60 seconds. What is the runner's average velocity?
   1. 6.67 m/s
   2. 0 m/s
   3. 6.67 m/s in the direction of running
   4. 400 m/s
6. An object is dropped from a height of 45 meters. Assuming acceleration due to gravity is 10 m/s², how long will it take to reach the ground?
   1. 3 seconds
   2. 4.5 seconds
   3. 9 seconds
   4. 2.12 seconds
7. A particle's position is given by $x(t) = 3t^2 - 2t + 1$. What is its velocity at t = 2 seconds?
   1. 8 m/s
   2. 10 m/s
   3. 11 m/s
   4. 4 m/s