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 ${\mu }_s$

Answer 1

Consider the problem
Let

Initial speed $=v$

and

Final speed $=u$

according to question

$Forceacting=frictionalforce$

therefore,

$ma={\mu }_{s}mg$

then

$a={\mu }_{s}g$

consider traveled is $d$.

therefore,

$u^2-v^2=2ad$

So,

$0^2-v^2=2ad$ (final speed is $0$)

$-v^2=2{\mu }_{s}gd$

$d=-\frac{v^2}{2\mu g}$

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