Question

A bus starts from rest with a constant acceleration of $5m/s^2$ . At the same time a car travelling with a constant velocity 50 m/s over takes and passes the bus .How fast is the bus travelling when they side by side?

• A. 10 m/s
• B. 50 m/s
• C. 100 m/s
• D. none

Answer 1

The correct option is C 100 m/s

Here, distance covered by bus will be equal to distance covered by car.

so, using newton's equation of motion,

$s=ut+\frac{1}{2}a{t}^2$......................(1)

so, $s=50t,u=0,a=5m/s^2$ , putting in equation (1),

$50t=0\ast t+\frac{1}{2}5t^2$

Solving for t,

we get, t=20 sec

Also, distance =speed *time

distance=50*20=1000m

Using Newton,s equation for motion,

$v^2-u^2=2as$

$v^2-0=2\ast 5\ast 1000$

$v^2=10000m/s^2$

$v=100m/s$

Correct answer is C.