Question

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

Answer 1

Let the cyclist overtake in t s
For the bus,
u=0.
in t s,
bus travels d= it+0.5 at^2
=>d= 0+0.5×2×t^2
=>d=t^2

For the cyclist distance travelled s= vt=> s= 20t
according to the problem,
20t+96=t^2
=> t^2-20t-96=0
On solving we get,
t=8s.

Please check the answer and let me know..