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  4. A car of mass m, travelling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is same for both cases, what time would be required to stop a car of mass 2 m travelling at speed v?

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Q. A car of mass $m$, travelling at speed $v$, stops in time $t$ when maximum braking force is applied. Assuming the braking force is same for both cases, what time would be required to stop a car of mass $2 \,m$ travelling at speed v?

Motion in a Straight Line

Solution:

Let the acceleration of first car be a.
Then acceleration of second car is.
For first car, $0 = v - at $ or $ t = \frac{v}{a}$
For second car, $ 0 = v -\frac{a}{2} t'$ or
$ t' = \frac{2v}{a} = 2t$