Answer to Question #137746 in Classical Mechanics for max

Question

A point traversed half the distance with a velocity v0. The remaining part of the distance was covered with velocity v1 for half the time, and with velocity v2 for the other half of the time. Find the mean velocity of the point averaged over the whole time of motion.

Answer 1

Solution

Consider that d is total distance covered by point and now half distance is covered in t time and other half is covered in 2t' time.

These are given by

$t=\frac{d}{2v_0}$ .................... eq. 1

$2t'=\frac{d}{v_1+v_2}$ . ................ eq. 2

So average velocity is given by

$<v>=\frac{d}{t+2t'}$

By putting the value of t and 2t'

$<v>=\frac{2v_0(v_1+v_2)}{(v_1+v_2+2v_0)}$