A bus is moving with a speed of 10m/s 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?

Options

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

Answer

D

Explanation

Suppose speed of scooter is `v_(S)` and speed of bus is `v_(B),` the relative displacement between scooter & bus is,
`x _(S) - x_(B) = ( x _(OS) -o_(OB)) + (v _(S) - v _(B))t `
When it overtakes `x _(S) -x_(B) =0`
`therefore 0=100 0+ (v _(S) -10) t`
`therefore (10 - v _(S))t = 1000`
`therefore 10 -v _(S) = (1000)/(t)`
` therefore 10 -v _(S) = (1000)/(100)`
`therefore v _(S) =20 m//s`