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A body moving along a straight line trav...

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 is

A

`4.0 m s^(-1)`

B

`6.0 m s^(-1)`

C

`3.8 m s^(-1)`

D

`2.4 m s^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
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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