AP Physics 1 exam questions on Δx = v₀t + ½at²

📚 Quick Study Guide

• 📏 Displacement (Δx): The change in position of an object. Measured in meters (m).
• 🚀 Initial Velocity (v₀): The velocity of the object at the beginning of the time interval. Measured in meters per second (m/s).
• ⏱️ Time (t): The duration of the motion. Measured in seconds (s).
• acceleration (a): The rate of change of velocity. Measured in meters per second squared (m/s²).
• 💡 The Formula: $\Delta x = v_0t + \frac{1}{2}at^2$ calculates displacement when initial velocity, time, and constant acceleration are known.
• 📝 When to Use: Use this formula when acceleration is constant and you need to find displacement, given initial velocity, time, and acceleration.
• ⚠️ Units are Key:** Ensure all units are consistent (meters, seconds) before plugging values into the formula.

Practice Quiz

1. A car starts from rest and accelerates at a constant rate of 3 m/s² for 4 seconds. What is the displacement of the car during this time?
   1. 24 m
   2. 12 m
   3. 36 m
   4. 48 m
2. An object is moving with an initial velocity of 5 m/s and accelerates at 2 m/s² for 3 seconds. What is the displacement of the object?
   1. 15 m
   2. 9 m
   3. 24 m
   4. 33 m
3. A ball is thrown with an initial velocity of 10 m/s and experiences a constant acceleration of -2 m/s² (deceleration) for 2 seconds. What is the displacement of the ball?
   1. 20 m
   2. 16 m
   3. 12 m
   4. 8 m
4. A train starts from rest and travels 100 meters with a constant acceleration of 0.5 m/s². How long did it take to travel this distance?
   1. 10 s
   2. 14.14 s
   3. 20 s
   4. 25 s
5. An airplane accelerates from 20 m/s to 40 m/s over a distance of 200 meters. Assuming constant acceleration, what is the acceleration of the plane?
   1. 2 m/s²
   2. 3 m/s²
   3. 4 m/s²
   4. 6 m/s²
6. A car is traveling at 30 m/s when the brakes are applied, producing a constant deceleration of -5 m/s². What distance does the car travel before coming to a complete stop?
   1. 45 m
   2. 60 m
   3. 90 m
   4. 120 m
7. A rocket accelerates from rest at a rate of 10 m/s² for 5 seconds. What is the displacement of the rocket during this time?
   1. 25 m
   2. 50 m
   3. 125 m
   4. 250 m