Question

A train travels at a speed of 60 km h-1 from station A to station B and then comes back at a speed of 80 km h-1 from station B to station A. Find — (i) the average speed, and (ii) the average velocity of the train.

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Answer

(i) Avg speed = Total\ Distance\over Total\ time

From, A to B

speedAB = 60 km h-1

distance travelled = dAB = d

time taken = d/60

From, B to A

speedBA = 80 km h-1

distance travelled = dBA = d

time taken = d/80

Total distance travelled = d + d = 2d

Total time = d/60 + d/80

Avg speed = 2d\over{d\over 60}+{d\over 80}

Avg speed = 2d\over{4d+3d\over 240}

Avg speed = 2d\over{7d\over 240}

Avg speed = 2 × 240\over 7

Avg speed = 480\over 7

Avg speed = 68.57 km h-1

Hence, Avg Speed = 68.57 km h-1

(ii) Average velocity = displacement\over total\ time

As the train starts from station A and comes back to same station, hence, displacement is zero.

Therefore, the average velocity is also zero.

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