Attempt 4 A 0.250 kg toy car moving with a speed of 0.820 m/s collides with a wall. The figure shows the force exerted on the car by the wall over the course of the collision. What is the magnitude of the velocity, or final speed, of the car after the collision?

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Chapter9: Linear Momentum And Collisions
Section: Chapter Questions
Problem 37P: The figure below shows a bullet of mass 200 g traveling horizontally towards the east with speed 400...
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**Collision of a Toy Car with a Wall: Analysis of Force and Velocity**

**Scenario Description:**
A 0.250 kg toy car is moving at a speed of 0.820 m/s when it collides with a wall. The figure provided shows the force exerted on the car by the wall over the duration of the collision. The task is to determine the magnitude of the velocity, or final speed, of the car after the collision.

**Graph Analysis:**
The graph depicts the force exerted (in Newtons) on the y-axis, ranging from 0 to 40 N, and the time duration of the collision (in seconds) on the x-axis, ranging from 0 to 0.02 seconds.

- The force starts at 0 N and sharply increases to 40 N at around 0.01 seconds.
- After reaching the peak force of 40 N, it declines back to 0 N by 0.02 seconds.
  
This indicates a rapid increase and decrease in force over a short time interval, characteristic of a short-duration impact.

**Final Speed Calculation:**
The provided final speed (or magnitude of velocity) after the collision is entered as 0.684 m/s, which was marked as incorrect.

To approach solving this:
1. Calculate the impulse exerted on the car using the area under the force-time graph.
2. Use the impulse-momentum theorem \( \Delta p = J \) where \( \Delta p \) is the change in momentum and \( J \) is the impulse.
3. Determine the final velocity using the change in momentum and the mass of the car.

**Important Note:**
Students are encouraged to correctly interpret the force-time graph to compute the impulse and use it to find the correct final velocity of the toy car after the collision. The initial velocity is given, so applying the principles of physics will give the accurate final speed.
Transcribed Image Text:**Collision of a Toy Car with a Wall: Analysis of Force and Velocity** **Scenario Description:** A 0.250 kg toy car is moving at a speed of 0.820 m/s when it collides with a wall. The figure provided shows the force exerted on the car by the wall over the duration of the collision. The task is to determine the magnitude of the velocity, or final speed, of the car after the collision. **Graph Analysis:** The graph depicts the force exerted (in Newtons) on the y-axis, ranging from 0 to 40 N, and the time duration of the collision (in seconds) on the x-axis, ranging from 0 to 0.02 seconds. - The force starts at 0 N and sharply increases to 40 N at around 0.01 seconds. - After reaching the peak force of 40 N, it declines back to 0 N by 0.02 seconds. This indicates a rapid increase and decrease in force over a short time interval, characteristic of a short-duration impact. **Final Speed Calculation:** The provided final speed (or magnitude of velocity) after the collision is entered as 0.684 m/s, which was marked as incorrect. To approach solving this: 1. Calculate the impulse exerted on the car using the area under the force-time graph. 2. Use the impulse-momentum theorem \( \Delta p = J \) where \( \Delta p \) is the change in momentum and \( J \) is the impulse. 3. Determine the final velocity using the change in momentum and the mass of the car. **Important Note:** Students are encouraged to correctly interpret the force-time graph to compute the impulse and use it to find the correct final velocity of the toy car after the collision. The initial velocity is given, so applying the principles of physics will give the accurate final speed.
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