A 0.300 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 vall over the course of the collision. What is the magnitude of the velocity, or final speed, of the car after the collision? final speed = m/s TOOLS 45- x10 0.01 0.02 0. Time (s) Force (N)

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Chapter1: Units, Trigonometry. And Vectors
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**Collision Analysis of a Toy Car**

A 0.300 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.

**Problem Statement:**

What is the magnitude of the velocity, or final speed, of the car after the collision?

**Graph Analysis:**

- **X-Axis (Time, s):** The time interval ranges from 0 to 0.02 seconds.
- **Y-Axis (Force, N):** The force exerted is measured from 0 to 45 Newtons.
- **Graph Description:** The force applied to the car increases linearly, reaches a maximum of 45 N at approximately 0.01 seconds, and then decreases linearly back to zero at 0.02 seconds. This creates a triangular shape.

**Calculation:**

To find the final speed of the car, consider using the impulse-momentum theorem, which relates the change in momentum to the impulse experienced. The area under the force-time graph will give the impulse.

\[ \text{Impulse} = \Delta p = F \cdot \Delta t \]

Calculate the area under the triangular force-time graph to determine the impulse, then use it to find the change in velocity.

**Final Speed Calculation Box:**

\[ \text{Final Speed} = \quad \text{m/s} \]

**Note:** Ensure to integrate or calculate the area of the triangle for accurate results. Use tools like calculators for numerical computations.
Transcribed Image Text:**Collision Analysis of a Toy Car** A 0.300 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. **Problem Statement:** What is the magnitude of the velocity, or final speed, of the car after the collision? **Graph Analysis:** - **X-Axis (Time, s):** The time interval ranges from 0 to 0.02 seconds. - **Y-Axis (Force, N):** The force exerted is measured from 0 to 45 Newtons. - **Graph Description:** The force applied to the car increases linearly, reaches a maximum of 45 N at approximately 0.01 seconds, and then decreases linearly back to zero at 0.02 seconds. This creates a triangular shape. **Calculation:** To find the final speed of the car, consider using the impulse-momentum theorem, which relates the change in momentum to the impulse experienced. The area under the force-time graph will give the impulse. \[ \text{Impulse} = \Delta p = F \cdot \Delta t \] Calculate the area under the triangular force-time graph to determine the impulse, then use it to find the change in velocity. **Final Speed Calculation Box:** \[ \text{Final Speed} = \quad \text{m/s} \] **Note:** Ensure to integrate or calculate the area of the triangle for accurate results. Use tools like calculators for numerical computations.
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