A particle travels along a straight line. It covers halg the distance with a speed (v). The remaining part of the distance was covere with speed `v_(1)` for half the time and with speed `v_(2)` for the other half the time . Find the average speed of the particle over the entire motion.

Explanation

Let S = Total distance traversed by the particle `t_1` = time taken to travel half the distance (S/2) `v_0` =speed of the particle.
Now ,distance =speed x time `" "therefore " "(S)/(2) =v_0t_1 " "or " "t_1 =(S)/(2v_0) " "...(1)`
Now, let 2t be the time to cover the remaining distance ` (S)/(2) `Let t be the time taken by the particle to travel distance with speed