A bus starts moving with an acceleration of $2m/s^2$. A cyclist 96m behind the bus starts simultaneously towards the bus at 20m/s. After what time will he be able to overtake the bus?

The correct option is B

8s

In t seconds bus travels a distance of x meters and boy travels (96+ x) meters

for bus,

$x=\frac{a{t}^2}{2}=\frac{2\times t^2}{2}=t^2$.....................................(1)

for boy,

x+96 = vt

x+96 = 20t ......................................................(2)

using (1) and (2),

$t^2$ - 20t + 96 = 0

we get t = 12 and 8,

Boy will catch the bus at t = 8 seconds.