Question

A bus starts from rest with a constant acceleration of 5m/s². Al the same time a car travelling with a constant velocity of 50m/s overtakes and passes the bus.
(i)Find at what distance will the bus overtake the car?
(ii)How fast will the bus be travelling then?


Class 11 motion in a straight line

Answer 1

Let after time t the bus will over the car.

let s be the distance travelled by the bus to overtake the car.

For bus : As a = 5 m/s^2 ; u = 0 m/s

so, s = u t + 1/2 a t^2

or, s = 0 + 1/2 ×5 × t^2

so, s = 5/2 t^2

Also, the distance travelled by the car in the same time t with v = 50 m/s

d = v t = 50 × t

As both s and d is the same distance

so, s = d

or, 5/2 t^2 = 50 t

or, t^2 - 20 t = 0

or, t ( t - 20 ) = 0

so, t = 20 s ; { 0 s neglected }

a) hence after s or d distance the bus will overtake the car

so, d = 50 × t = 50 × 20 = 1000 m

b) also v = u + a t

so, velocity of bus after 20 s

v = 0 + 5 × 20 = 100 m/s

the bus will be travelling then at a speed of

100 m/s.