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

Solution

## The correct option is C 100 m/sHere, distance covered by bus will be equal to distance covered by car.so, using newton's equation of motion,$$s=ut+\dfrac{1}{2}at^2$$......................(1)so, $$s=50t, u=0 ,a=5m/s^2$$ , putting in equation (1),$$50t=0*t+\dfrac{1}{2}5t^2$$Solving for t,we get, t=20 secAlso, distance =speed *time          distance=50*20=1000m Using Newton,s equation for motion,$$v^2-u^2=2as$$$$v^2-0=2*5*1000$$$$v^2=10000 m/s^2$$$$v=100m/s$$Correct answer is C.Physics

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