Question

A driver of a car travelling at 52 kmh^-1 applies the brakes and accelerates uniformly in the opposite direction. The car stops after 5 s. Another driver going at 34 kmh^-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 two cars. Which of the two cars travelled farther after the brakes were applied? 

Answer 1

In in the following graph, AB and CD are the time graphs for the two cars whose initial speeds are 52 km/h(14.4 m/s) and 34 km/h(8.9 m/s), respectively.

Distance covered by the first car before coming to rest 

= Area of triangle AOB 

= ½ × AO × BO 

= ½ × 52 kmh-1 × 5 s 

= ½ x (52 × 1000 × 1/3600) ms-1 × 5 s = 36.1 m 

Distance covered by the second car before coming to rest 

= Area of triangle COD 

= ½ × CO × DO 

= ½ × 34 km h-1 × 10 s 

= ½ × (34 × 1000 × 1/3600) ms-1 ×10 s = 47.2 m 

Thus, the second car travels farther than the first car after they applied the brakes.