Question

A bus starts moving with acceleration `2 ms^-2`. A cyclist `96 m` behind the bus starts simultaneously towards the bus at a constant speed of `20 m//s`. After what time will he be able to overtake the bus ?
A. 4 s
B. 8 s
C. 12 s
D. 16 s

Answer 1

Correct Answer - B
Let at time `t`,, the cyclist overtakes the bus, then
`96 +`(distance traveled by bus in time t)
=`("distance traveled by cyclist in time t")`
`rArr (1)/(2) xx 2 xx t^2 + 96 = 20 xx t`
`rArr t^2 - 20t + 96 = 0`
This gives, `t = 8 s` or `12 s`. Hence, the cyclist will overtake the bus in `8 s`.