Question

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

• A. 0, 0
• B. 0, 10 m/s
• C. 10 m/s, 20 m/s
• D. 20 m/s, 0

Answer 1

The Correct Option is B

To find the average velocity and average speed for each circular lap, we need to understand the definitions and apply the formulas correctly.

1. Average Speed:
   • Average speed is calculated as the total distance traveled divided by the total time taken.
   • For a circular track, the circumference C is given by the formula: C = 2 \pi R, where R is the radius.
   • Given the radius R = 100 \, \text{m}, the circumference of the circular track is: C = 2 \times \pi \times 100 = 628 \, \text{m}.
   • The car takes 62.8 seconds to complete one lap.
   • Therefore, the average speed is: \text{Average Speed} = \frac{628 \, \text{m}}{62.8 \, \text{s}} \approx 10 \, \text{m/s}.
2. Average Velocity:
   • Average velocity is calculated as the total displacement divided by the total time taken.
   • Displacement is the shortest distance between the starting and ending points.
   • For a complete lap on a circular track, the starting and ending points are the same, resulting in zero displacement.
   • Therefore, the average velocity for each complete lap is: \text{Average Velocity} = \frac{0 \, \text{m}}{62.8 \, \text{s}} = 0 \, \text{m/s}.
3. Conclusion: Based on the calculations,
   • The average velocity is 0 \, \text{m/s}.
   • The average speed is 10 \, \text{m/s}.
   • Therefore, the correct answer is:
     0, 10 m/s
     .