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?

To plot the speed versus time graphs for the two cars, we’ll first convert the speeds from km/h to m/s (since the time is given in seconds) and then illustrate the deceleration of the cars.

Given:
– Car 1: Initial speed v1 = 52 km/h, Time to stop t1 = 5 s
– Car 2: Initial speed v2 = 3 km/h, Time to stop t2 = 10 s

Converting speeds to m/s:
– Car 1: v1 = 52km/h = ((52 x 1000) x (3600)) m/s ≈ 14.44 m/s
– Car 2: v2 = 3km/h = ((3 x 1000) x (3600))m/s}\) ≈ 0.83 m/s

Now, let’s plot the speed versus time graphs for both cars:

Graph:
– Car 1 (Deceleration):
– Starts at 14.44 m/s
– Decelerates uniformly until 0 m/s in 5 seconds.

– Car 2 (Deceleration):
– Starts at 0.83 m/s
– Decelerates uniformly until 0 m/s in 10 seconds.

The area under the speed-time graph represents the distance covered.
– Car 1’s Area: 1/2 x (initial speed + final speed) x time = 1/2 x (14.44m/s + 0 m/s) x 5 s = 36.1m
– Car 2’s Area: 1/2 x (initial speed + final speed) x time = 1/2 x (0.83 m/s + 0 m/s x 10 s = 4.15m

Conclusion:
Car 1, despite having a higher initial speed, covered a greater distance after the brakes were applied. Car 1 traveled approximately 36.1 meters, while Car 2 covered approximately 4.15 meters before coming to a stop.