Train A is travelling at a speed of $54 km / h$ . It applies brakes and retards uniformly for $5 s$ and then stops. Similarly, Train B is travelling at a speed of $36 km / h$ and it applies brakes and retards uniformly for $10 s$ and then stops. Which of the trains travelled farther?

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Train A

Train B

Both stopped at the same point

None of the above

answer is B.

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Detailed Solution

Train A is travelling at a speed of $54 km / h$ . It applies brakes and retards uniformly for $5 s$ and then stops. Similarly, Train B is travelling at a speed of $36 km / h$ and it applies brakes and retards uniformly for $10 s$ and then stops. Train B travelled farther.
Converting Speeds of both trains to $m / s .$
Speed of Train A $= 54 km / h \times \frac{5}{18}$
                             $= 15 m / s$
Speed of Train B $= 36 km / h \times \frac{5}{18}$
                             $= 10 m / s$
Now, plot the velocity-time graph of both the trains.
So, Distance travelled by train A $=$ Area under line RS
                                                      $= 0.5 \times 15 \times 5$
                                                      $= 37.5 m$
Distance travelled by train B $=$ Area under line PQ
                                                $= 0.5 \times 10 \times 10$
                                                $= 50 m$
Hence, Train B travelled the farthest.