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प्रश्न
A train travels with a speed of 60 km h-1 from station A to station B and then comes back with a speed 80 km h-1 from station B to station A. Find -
- The average speed
- The average velocity of the train.
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उत्तर
(i) Given,
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 ...[Eqn. 1]
Total time = `"d"/60 + "d"/80` ...[Eqn. 2]
Substituting the values from the equations 1 and 2 in the formula we get,
Average speed = `"Total Distance"/"Total time"`
= `"2d"/("d"/60 + "d"/80)`
= `"2d"/(("4d" + "3d")/240)`
= `("2d"/"7d")/240`
= `(2/7)/240`
= `(2 xx 240)/7`
= `480/7`
= 68.57 km h-1
Hence, Average Speed = 68.57 km h-1
(ii) Average velocity = `"Displacement"/"total time taken"`
Because the train starts and ends at the same station, the displacement is zero. Thus the average velocity is zero.
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