Question

A bus starts from rest with constant acceleration of 5 m/s×s.At the same time a car travelling with a constant velocity 50m/s over takes tales and passes the bus.How fast isbthe bis travelling when they are side by side?

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 }

As 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.

Answer 2

Answer:

DISTANCE COVERED BY CAR WILL EQUAL TO THE DISTANCE COVERED BY BUS.

SO,

UT + 1/2 AT² = 50T

0×T+1/2×5×T² = 50T

5/2 T² = 50T

5/2 T = 50

T = 50×2/5

T = 20 SECONDS

DISTANCE = SPEED × TIME

DISTANCE = 50 × 20

DISTANCE = 1000 METRES

USING 3RD EQUATION OF UNIFORMLY ACCELERATED MOTION,

V² = U² + 2AS

V² = 0² + 2×5×1000

V² = 10×1000

V = √10000

V = 100 M/S