The driver of train A travelling at a speed of 54 kmh-1 applies brakes and retards the train uniformly. The train stops in 5 seconds. Another train B is travelling on the parallel with a speed of 36 kmh-1 . Its driver applies the brakes and the train retards uniformly; train B stops in 10 seconds. Plot speed-time graphs for both the trains on the same axis. Which of the trains travelled farther after the brakes were applied?

For train A, the initial velocity,

u = 54 kmh^-1 = 54 × {5\over18}= 15 ms^-1

Final velocity, v = 0     and time, t = 5s

For train B, u = 36 kmh^-1 = 36 x{5\over18} = 10 ms^-1

v = 0;    t =10 s

Speed-time graph for train A and B are shown in the figure.

Distance travelled by train A

= Area under straight line graph RS

= Area of ΔORS

= {1\over2} x OR x OS

= {1\over2} x 15ms^-1 x 5s

= 37.5 m

Distance travelled by train B = Area under PQ = Area of ΔOPQ

={1\over2} x OP x OQ

={1\over2} x 10ms^-1 x 10s = 50m

Thus, train B travelled farther after the brakes were applied.