Question

A driver of a car traveling 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 traveled farther after the brakes were applied?

Answer 1

Step1: Given data

A driver of a car traveling at $52km{h}^{-1}$ applies the brakes and accelerates uniformly in the opposite direction. The car stops in $5s$. Another driver going at $3km{h}^{-1}$ in another car applies his brakes slowly and stops in $10s$.

Step2: Formula used

$s=\left(\frac{u+v}{2}\right)t[wheres=dis\tan ce,u=initialvelocity,v=finalvelocity,t=time]$

Step3: Calculating the distance of both the cars

Let us assume the first car is A.

The initial speed of the car A, $u=52km{h}^{-1}=52\times \frac{5}{18}=14.44m{s}^{-1}$

Car A sops in 5 seconds, $v=0att=5$

The initial speed of the car B, $u=3km{h}^{-1}=3\times \frac{5}{18}=0.83m{s}^{-1}$

Car B sops in 10 seconds, $v=0att=10$

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

The area under the speed-time graph gives the distance covered.
Distance covered by car A $s_A=\frac{1}{2}\times 14.44\times 5=36.1m$

Distance covered by car B $s_B=\frac{1}{2}\times 0.83\times 10=4.15m$

Thus car A travels more distance than B.