A body moving along a straight line travels one third of the total distance with a speed of `3.0 m s^(-1)`. The remaining distance is covered with a speed of `4.0 m s^(-1)` for half the time and `5.0 m s^(-1)` for the other half of the time. The average speed during the motion isA. `4.0 m s^(-1)`B. `6.0 m s^(-1)`C. `3.8 m s^(-1)`D. `2.4 m s^(-1)`

A body moving along a straight line travels one third of the total dis

1.	A body moving along a straight line travels one third of the total distance with a speed of `3.0 m s^(-1)`. The remaining distance is covered with a speed of `4.0 m s^(-1)` for half the time and `5.0 m s^(-1)` for the other half of the time. The average speed during the motion isA. `4.0 m s^(-1)`B. `6.0 m s^(-1)`C. `3.8 m s^(-1)`D. `2.4 m s^(-1)`
Answer» Correct Answer - C Let S be the total distance travelled by the body. Let `t_1` be the time taken to cover the first one third of the distance. Then `t_1 = (S/3) / 3 = S/9` Let `t_2` be the time taken for each of the remaining two journeys. Then `S-S/3 = 4t_2 + 5t_2` or `(2S)/3 = 9t_2` or `t_2 = (2S)/27` Average speed = Total distance travelled / Total time taken `= S/t_1 + 2t_2` `= (S)/(S/9) + 2xx(2S)/27 = 3.8 m s^(-1)`

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