A driver of a car travelling at $52$km $h^{-1}$ applies the brakes and accelerates uniformly in the opposite direction. The car stops in $5$s. Another driver going at $3$km $h^{-1}$ in another car applies his brakes slowly and stops in $10$s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?

(A) : Initial speed of the car A $u=52$ $km{h}^{-1}=52\times \frac{5}{18}=14.44$ $m{s}^{-1}$

The car stops in 5 seconds i.e $v=0$ at $t=5$

(A) : Initial speed of the car A $u=3$ $km{h}^{-1}=3\times \frac{5}{18}=0.83$ $m{s}^{-1}$

The car stops in 10 seconds i.e $v=0$ at $t=10$

With the help of these initial and final points for both the cases, we can plot the graph of speed vs time.

Area under the speed-time graph gives the distance covered.

$\therefore$ Distance covered by car A $x_A=\frac{1}{2}\times 14.44\times 5=36.1$ m

$\therefore$ Distance covered by car A $x_B=\frac{1}{2}\times 0.83\times 10=4.15$ m

Thus car A travels more distance than B.