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Question

A car is moving on a straight horizontal road with a speed v. When brakes are applied to give a constant retardation a, the car covers distance S before coming to rest. If the car were moving with a speed 3v and the same retardation a is applied, the distance that the car travels will be

A
3S
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B
6S
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C
9S
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D
27S
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Solution

The correct option is C 9S
Acceleration =a (i.e retardation)
The shortest stopping distance S is given by
0v2=2aS (From third equation of motion)
or S=v22a.
Thus, for a given value of a,Sv2.
If v is increased by a factor of 3, S will increase by a factor (3)2=9.
Hence the correct choice is (c).

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