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 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 is
Answer» `4.0 m s^(-1)` `6.0 m s^(-1)` `3.8 m s^(-1)` `2.4 m s^(-1)` Solution :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)`