A student is standing at a distance of `50` metres from a bus. As soon as the bus begins its motion (starts moving away from student) with an acceleration of `1 ms^-2`, the student starts running towards the bus with a uniform velocity `u` . Assuming the motion to be along a straight road. The minimum value of `u`, so that the student is able to catch the bus is :

Options

A. `5ms^(-1)`
B. `8ms^(-1)`
C. `10ms^(-1)`
D. `12ms^(-1)`

Answer

C

Explanation

`ut = 50 + 1/2 xx a xx t^2`
`rArr ut = 50 + 1/2 xx 1 xx t^2 rarr u = (50)/(t) + t/2`
Fom minimum velocity `(du)/(dt) = 0`
`rArr (-50)/(t^2) + 1/2 = 0 rArr t = 10 sec`
`u_("min") = 10 m//s`