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Question

A student is standing at a distance of 50 metres from the bus. As soon as the bus begins its motion with an acceleration of 1 m/s−2 , 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 ms1
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B
8 ms1
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C
10 ms1
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D
12 ms1
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Solution

The correct option is C 10 ms1

Let student will catch the bus after t sec. So it will cover distance ut.

Similarly distance travelled by the bus will be 12at2 for the given condition.

ut=50+12at2=50+t22 [a=1 m/s2]

u=50t+t2
To find the minimum value of u.
dudt=0,so we get t=10 sec, then u = 10 m/s


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