Question

Question 5
A driver of a car travelling at 52 kmph applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 seconds. Another driver going at 3 kmph in another car applies his brakes slowly and stops in 10 seconds. 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?

Answer 1

As given in the figure below PR and SQ are the speed-time graphs for given two cars with initial speeds $52kmph$ and $3kmph$ respectively.
$52kmph=52\times \frac{5}{18}=14.44m{s}^{-1}$ and $3kmph=3\times \frac{5}{18}=0.833m{s}^{-1}$
The speed time graph is plotted as below:



Distance traveled by first car before coming to rest = Area of $\Delta$ OPR
$=\frac{1}{2}\times OR\times OP$
$=\frac{1}{2}\times 5\times 14.44$
$=36.11m$

Distance traveled by second car before coming to rest = Area of $\Delta$ OSQ
$=\frac{1}{2}\times OQ\times OS$
$=\frac{1}{2}\times 10\times 0.833$
=$4.165m$
So the first car traveled larger distance after the brakes were applied.