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Question

The same retarding force is applied to stop a train, if the speed is doubled then the stopping distance will be

A
same
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B
doubled
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C
half
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D
four times
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Solution

The correct option is D four times
We know that s=(v2u2)2a (negative sign for retarding force)
Since force is constant, thus acceleration is constant.
In first case with speed u, it stops when v=0, thus s=(0u2)2a=u22a
In second case with speed = 2u, s=(0(2u)2)2a=4u22a
Thus it is 4 times

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