A car turns at a constant speed on a circular track of radius $100 ext{ m}$, taking $62.8 ext{ s}$ for eve

Question

A car turns at a constant speed on a circular track of radius $100 	ext{ m}$, taking $62.8 	ext{ s}$ for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

Accepted Answer

1. **Average Velocity:** Average velocity is defined as the ratio of total displacement to the total time interval ($v_{avg} = \Delta x / \Delta t$) . For one complete circular lap, the car returns to its initial position. Therefore, the net displacement $\Delta x$ is zero. Consequently, the average velocity is zero.
2. **Average Speed:** Average speed is defined as the ratio of the total path length to the total time interval . The path length for one lap is the circumference of the circle, $2\pi R$.
3. **Calculation:**
   - Radius $R = 100 	ext{ m}$.
   - Time $t = 62.8 	ext{ s}$.
   - Path Length = $2\pi R = 2 	imes 3.14 	imes 100 = 628 	ext{ m}$.
   - Average Speed = $\frac{628}{62.8} = 10 	ext{ m/s}$.
4. **Conclusion:** The average velocity is 0 and the average speed is $10 	ext{ m/s}$.

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