Question

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

Answer 1

Let's first convert the speeds to SI unit.
$v_1=52km/h=52\times \frac{1000}{3600}m/s$
$v_1=14.44m/s$
[0.5 Mark]
$v_2=3km/h=3\times \frac{1000}{3600}m/s$
$v_2=0.83m/s$
[0.5 Mark]

Plotting the information, we get the following graph:
[1 Mark]

The area under the speed-time graph is equal to the distance moved by the cars. Clearly, the area is larger for the first car (initial speed of 52 km/h). Hence, it moved a larger distance.
[1 Mark]