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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
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B
50 m/s
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C
100 m/s
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D
none
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Solution

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,
$$s=ut+\dfrac{1}{2}at^2$$......................(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 sec
Also, 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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