Question

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

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

Answer 1

The correct option is B

$0,10m/s$

Step 1: Given

Radius of the track, $r=100m$

Time, $t=62.8seconds$

Step 2: Formula used

1. $Averagevelocity=\frac{Displacement}{time}$
2. $Averagespeed=\frac{Dis\tan cecovered}{time}$

Step 3: Determine the average velocity

As the track is circular, the total displacement will be zero.

Displacement is the shortest distance covered. And in the case of a circular path, the initial and final points coincide. Hence, the shortest distance will be zero.

$$\begin{gathered} Averagevelocity=\frac{Displacement}{time} \\ =\frac{0}{62.8} \\ =0 \end{gathered}$$

Step 4: Determine the average speed

The distance covered will be the circumference of the track.

$$\begin{gathered} Averagespeed=\frac{Trackcircumference}{time} \\ =\frac{2\mathrm{\pi r}}{t} \\ =\frac{2\times 3.14\times 100}{62.8} \\ =10m/s \end{gathered}$$

Hence, option B is the correct option.