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Question

A student is standing at a distance of 50 meters from the bus. As soon as the bus starts its motion with an acceleration of 1ms, the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is

A
5 ms
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B
8 ms
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C
10 ms
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D
12 ms
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Solution

The correct option is C 10 ms
Let, the student catches the bus after t sec. So, it will cover distance ut.

Similarly, distance travelled by the bus will be 12at2. Therefore, for the given condition
ut=50+12 at2=50+t22u=50t+t2(as a=1 ms2)....(1)

So, to find the minimum value of u, dudt=0,d(50t+t2)dt=050t2+12=0t2=100t=10 s

Then putting value of t in equation (1), we get u=10 ms

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