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Question

An automobile is moving on a straight horizontal road with speed u. What is the shortest distance in which the automobile can be stopped? Take the coefficient of static friction between the tyres and the road as μs

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Solution

Consider the problem
Let
Initial speed =v
and
Final speed =u
according to question

Forceacting=frictionalforce
therefore,
ma=μsmg
then
a=μsg
consider traveled is d.
therefore,
u2v2=2ad
So,
02v2=2ad (final speed is 0)
v2=2μsgd
d=v22μg

Where negative sign indicates that force acts in the opposite direction of the force.

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