Explanation

(c) There is a static friction between tyres and road, so frictional force cause the retardation in velocity of a automobile.
[image:5_image199.jpeg]
Free body diagram of automobile is shown. From Newton’s third law
$F = f_{s} = \mu\ R = \mu\ mg$
Where $m$ is the mass of automobile.
Also, $F = ma$
$ma = \mu\ mg$
$\Longrightarrow \ \ a = retardation = \mu\ g = 0.5\ g$
Let automobile stops at a distance $x$, then from equation of motion
$v^{2} = v^{2} - 2\ ax$
$Given,,v = 0,u = {72\ kmh}^{- 1} = 72 \times \frac{5}{18}{ms}^{- 1} = {20\ ms}^{- 1},$
$g = 9.8\ {ms}^{- 2}$
$\therefore\ \ 0^{2} = (20)^{2} - 2 \times 0.5 \times 9.8x$
$\Longrightarrow \ \ \ x = \frac{20 \times 20}{2 \times 0.5 \times 9.8} = 40.8\ m$