Question

Sohail cycles on a circular track in an anticlockwise direction as shown in the figure. He travels with a speed ‘V’ to cover the path AB, next with speed ‘2V’ from B to C and with a speed of ‘3V’ from C to A. What is his average speed for the total journey?

• A. 2V
• B. 6V
• C. 3V
• D. $\frac{V}{2}$

Answer 1

The correct option is A

2V

We know, average speed = $\frac{Totaldistance}{Totaltime}$

Total distance = $2\pi r$; where 'r' is the radius of the circle.

Total time = time taken in going from A to B + time taken in going from B to C + time taken in going from C to A.

Time taken to travel from A to B = $\frac{Distance}{Speed}$

Distance covered in going from A to B = length of arc AB

So, length of arc AB = $2\pi r\left(\frac{60}{360}\right)=\frac{\pi r}{3}$

Time is taken in going from A to B = $\frac{\frac{\pi }{3}.r}{V}$

Similarly, time is taken in going from B to C = $\frac{\frac{2\pi }{3}.r}{2V}$

And time is taken in going from C to A = $\frac{\pi r}{3V}$

Total time = $\frac{\frac{\pi }{3}.r}{V}+\frac{\frac{2\pi }{3}.r}{2V}+\frac{\pi r}{3V}$ = $\frac{\pi r}{V}$

Average speed = $\frac{2\pi r}{\frac{\pi r}{V}}=2V$