Question

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 :
A. `5 ms^-1`
B. `8 ms^-1`
C. `10 m//s^-1`
D. `12 m//s^-1`

Answer 1

Correct Answer - C
`50 + x = ut` …(1) and `x = (t^2)/(2)`….(2)
From (1) and (2)
`50 + (t^2)/(2) = ut rArr t^2 - 2ut + 100 = 0`
For real roots, discriminant = 0
For minimum velocity, discriminant = 0
`rArr 4 u^2 - 400 = 0 rArr u = 10 m//s`.