A bus is moving with a speed of `10 m s^(-1)` on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooteritst with what speed should the scooterist chase the bus?

Options

A. `40 m s^(-1)`
B. `25 m s^(-1)`
C. `10 m s^(-1)`
D. `20 m s^(-1)`

Answer

D

Explanation

Let `v_1` be the velocity of scooter. The distance between the scooter and the bus = 1 km = 1000 m.
The velocity of bus, `v_b = 10 m s^(-1)`
Time taken to overtake the bus, t = 100 s.
Relative velocity of the scooter w.r.t the bus `= (v_s- 10)`
`therefore t = 1000/(v_s - 10) = 100` or `v_s = 20 m s^(-1)`