Question

A car travels along a circular track of a radius of 50 m. It takes 20 seconds to complete one rotation.

Calculate (i) speed (ii) Velocity of the car .

Answer 1

Step 1: Given that

Radius of circular track = 50 m.

Time = 20 seconds .

Step 2: Formula

$Speed=\frac{Dis\tan ce}{Timetaken}$

$Dis\tan ce=2\times \mathrm{\pi }\times \mathrm{r}$

$Speed=\frac{2\times \mathrm{\pi }\times \mathrm{r}}{t}$

$Velocity=\frac{Displacement}{Timetaken}.$

Step 3:Calculation :

(i) Speed

$Dis\tan ce=2\times \mathrm{\pi }\times \mathrm{r}.$

$$\begin{gathered} Dis\tan ce=2\times 3.14\times 50m. \\ Dis\tan ce=314m. \end{gathered}$$

$$\begin{gathered} Speed=\frac{314m}{20s}=15.7\frac{m}{s}. \\ Speed=15.7\frac{m}{s}. \end{gathered}$$

(ii) Velocity of the car .

As the car traveled along a circular path so the displacement of the body is zero.

Therefore, the velocity is zero.

Step 4 :

Hence,

(i) speed = $15.7\frac{m}{s}.$

(ii) Velocity of the car = Zero