To calculate the distance the car travels during its deceleration, we use the relationship between the angular motion of the tires and the linear distance covered by the car.

Step 1: Linear distance covered by the car

The relationship between linear distance $d$, angular displacement $\theta$, and the radius of the tire $r$ is: $d = r \cdot \theta$

Where:

• $d$ is the linear distance traveled.
• $r = 0.300 \, \text{m}$ is the radius of the tires.
• $\theta$ is the total angular displacement in radians.

Step 2: Convert revolutions to radians

The tires made $31.2$ revolutions before stopping. Since one revolution equals $2\pi$ radians, the total angular displacement is: $\theta = 31.2 \cdot 2\pi = 62.4\pi \, \text{radians}$

Step 3: Calculate linear distance

Now, substitute $r$ and $\theta$ into the formula: $d = r \cdot \theta = 0.300 \cdot 62.4\pi$ $d \approx 0.300 \cdot 196.34954 = 58.90486 \, \text{m}$

Final Answer:

The car travels approximately: $\boxed{58.9 \, \text{m}}$

Let me know if you want further clarification on any step! 😊

---

Questions for deeper understanding:

1. How is the relationship between angular and linear motion derived?
2. What would happen to the distance if the radius of the tire were larger?
3. How is angular acceleration related to the time taken to stop?
4. Can you derive the angular displacement using kinematic equations?
5. How does this result compare with calculating distance from linear deceleration alone?

Tip:

Always double-check unit conversions, especially when dealing with angular measurements (radians vs. degrees).