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» <html><body><p>`4.0 m s^(-1)`<br/>`6.0 m s^(-1)`<br/>`3.8 m s^(-1)`<br/>`2.4 m s^(-1)`</p>Solution :<a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> S be the <a href="https://interviewquestions.tuteehub.com/tag/total-711110" style="font-weight:bold;" target="_blank" title="Click to know more about TOTAL">TOTAL</a> distance <a href="https://interviewquestions.tuteehub.com/tag/travelled-7256865" style="font-weight:bold;" target="_blank" title="Click to know more about TRAVELLED">TRAVELLED</a> by the body. Let `t_1` be the time taken to cover the first one third of the distance. Then <br/> `t_1 = (S/3) / 3 = S/9` <br/> Let `t_2` be the time taken for each of the remaining two journeys. Then <br/> `S-S/3 = 4t_2 + 5t_2` or `(2S)/3 = 9t_2`or`t_2 = (2S)/27` <br/> Average speed = Total distance travelled / Total time taken `= S/t_1 + 2t_2` <br/> `= (S)/(S/9) + 2xx(2S)/27 = 3.8 m s^(-1)`</body></html>