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The driver of a train $A$ travelling at a speed of $54\, km h^{-1}$ applies brakes and retards the train uniformly The train stops in $5\, s$. Another train $B$ is travelling on the parallel track with a speed of $36\, km h ^{-1}$. This driver also applies the brakes and the train retards uniformly. The train $B$ stops in $10\, s$. Plot speed time graph for both the trains on the same paper. Also, calculate the distance travelled by each train after the brakes were applied.
Solution
Given $u_{ A }=54 km h ^{-1}=54 \times 5 / 18=15 m s ^{-1}$
$t_{ A }=5 s , v_{ A }=0$
$u_{ B }=36 km h ^{-1}=36 \times 5 / 18=10 m s ^{-1}, t_{ B }=5 s$
$v_{ B }=0$
The two motions are shown graphically as below
Distance travelled by $A =$ Area under $AB$ graph $=1 / 2 \times 5 \times 15=37.5 m$
Distance travelled by $B =$ Area under $CD$ graph $=1 / 2 \times 10 \times 10=50 m$
