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Physics Question on Motion in a straight line

A bus is moving with a speed of 10 ms−110 \,ms^{-1} on a straight road. A scooterist wishes to overtake the bus in 100 s100 \,s . If the bus is at a distance of 1 km1 \,km from the scooterist with what speed should the scooterist chase the bus ?

A

40 ms−140 \,ms^{-1}

B

25 ms−125 \,ms^{-1}

C

10 ms−110 \,ms^{-1}

D

20 ms−120 \,ms^{-1}

Answer

20 ms−120 \,ms^{-1}

Explanation

Solution

Let vv, be the velocity of the scooter, the distance between the scooter and the bus =1000 m=1000\, m,
The velocity of the bus =10 ms−1=10\, ms ^{-1}
Time taken to overtake =100 s=100\, s
Relative velocity of the scooter with respect to the bus =(vs−10)=\left( v _{ s }-10\right)
1000/(vs−10)=100 s1000 /\left(v_{s}-10\right)=100\, s
=vs=20 ms−1=v_{s}=20\, ms ^{-1}