A bus starts moving with an acceleration `2 m//s^2`. A cyclist 96 m behind the bus starts simultaneously in the direction of the bus at a speed of 20 m/s. After what time the cyclist will overtake the bus?

Options

A. 16 s
B. 8 s
C. 12 s
D. 4s

Answer

C

Explanation

Say the cyclist catches the bus after time t. During t sec, bus travels a distance of `= 1/2 (2) t^2 = t^2m ` .
In the same time cyclist covers a distance 20 t.

So,
`96 + 1/2 a t^2 = 20 xx t`
`implies t^2 - 20 t + 96 = 0`
`implies t = (20 pm sqrt(400 - 4 xx 96))/(2 xx 1)`
`implies t = (20 pm 4)/2 = 12`