A bus starts from rest and moves with constant acceleration `8 m//s^(2)`. At the same time, a car traveling with a constant velocity `16 m//s` overtakes and passes the bus. After how much time and at what distance the bus overtakes the car?

Explanation

Let the bus overtake the car after time t and at distance `d`. Bus (accelerated motion):
`s=ut+1/2at^(2)`
`d=1/2xx8xxt^(2) …(i)`
Car (uniform motion):
`s=vt`
`d=16t …(ii)`
solving (i) and (ii), we get
`t=4 s, d=64m`