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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.
Question Image

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.

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