15. Go (a) Suppose that a NASCAR race car is moving to the right with a constant velocity of +82 m/s. What is the average acceleration of the car? (b) Twelve seconds later, the car is halfway around the track and traveling in the opposite direction with the same speed. What is the aver- age acceleration of the car?

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### Physics Problem: Calculating Average Acceleration

**Problem Statement:**

**15. (a)** Suppose that a NASCAR race car is moving to the right with a constant velocity of +82 m/s. What is the average acceleration of the car?

**(b)** Twelve seconds later, the car is halfway around the track and traveling in the opposite direction with the same speed. What is the average acceleration of the car?

**Solution Breakdown:**

1. **Understanding Velocity and Acceleration:**
   - Velocity is the speed of an object in a given direction.
   - Acceleration is the rate of change of velocity with respect to time.

2. **Part (a):**
   - Since the car is moving with a constant velocity of +82 m/s to the right, there is no change in speed or direction.
   - The average acceleration in this scenario is 0 m/s² because there is no change in velocity.

3. **Part (b):**
   - After 12 seconds, the car is now moving in the opposite direction with the same speed.
   - The initial velocity (v_i) is +82 m/s.
   - The final velocity (v_f) is -82 m/s (indicating the opposite direction).

   The change in velocity (Δv) = v_f - v_i = -82 m/s - (+82 m/s) = -164 m/s.

4. **Calculating Average Acceleration:**
   - Average acceleration (a) is given by the change in velocity (Δv) divided by the time taken (Δt).
   - Δt = 12 seconds.

    \[
    a = \frac{\Delta v}{\Delta t} = \frac{-164 \, \text{m/s}}{12 \, \text{s}} = -13.67 \, \text{m/s}^2
    \]

Therefore, the average acceleration of the car is -13.67 m/s². This negative sign indicates that the car is accelerating in the opposite direction to its initial velocity.
Transcribed Image Text:### Physics Problem: Calculating Average Acceleration **Problem Statement:** **15. (a)** Suppose that a NASCAR race car is moving to the right with a constant velocity of +82 m/s. What is the average acceleration of the car? **(b)** Twelve seconds later, the car is halfway around the track and traveling in the opposite direction with the same speed. What is the average acceleration of the car? **Solution Breakdown:** 1. **Understanding Velocity and Acceleration:** - Velocity is the speed of an object in a given direction. - Acceleration is the rate of change of velocity with respect to time. 2. **Part (a):** - Since the car is moving with a constant velocity of +82 m/s to the right, there is no change in speed or direction. - The average acceleration in this scenario is 0 m/s² because there is no change in velocity. 3. **Part (b):** - After 12 seconds, the car is now moving in the opposite direction with the same speed. - The initial velocity (v_i) is +82 m/s. - The final velocity (v_f) is -82 m/s (indicating the opposite direction). The change in velocity (Δv) = v_f - v_i = -82 m/s - (+82 m/s) = -164 m/s. 4. **Calculating Average Acceleration:** - Average acceleration (a) is given by the change in velocity (Δv) divided by the time taken (Δt). - Δt = 12 seconds. \[ a = \frac{\Delta v}{\Delta t} = \frac{-164 \, \text{m/s}}{12 \, \text{s}} = -13.67 \, \text{m/s}^2 \] Therefore, the average acceleration of the car is -13.67 m/s². This negative sign indicates that the car is accelerating in the opposite direction to its initial velocity.
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