Question

A bus is moving with a speed of $ 10 \,ms^{-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 scooterist with what speed should the scooterist chase the bus ?

• A. $ 40 \,ms^{-1} $
• B. $ 25 \,ms^{-1} $
• C. $ 10 \,ms^{-1} $
• D. $ 20 \,ms^{-1} $

Answer 1

Answer: (D)

Let $v$, be the velocity of the scooter, the distance between the scooter and the bus $=1000\, m$,
The velocity of the bus $=10\, ms ^{-1}$
Time taken to overtake $=100\, s$
Relative velocity of the scooter with respect to the bus $=\left( v _{ s }-10\right)$
$\therefore \frac{1000}{\left(v_{s}-10\right)}=100\, s $
$\Rightarrow v_{s}=20\, ms ^{-1}$