Answer to Question #137404 in Optics for Afraid

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

Let the total distance be d. Then for first half distance, time =$\frac{d}{2v_0}$

next distance time taken is $t_2=\frac{d}{4v_1}$

And the last half distance time is $t_3=\frac{d}{4v_2}$

Now Average speed $t=\frac{d}{\frac{d}{2v_0}+\frac{d}{4v_1}+\frac{d}{4v_2}}$

Thus $t=\frac{4v_0v_1V_2}{2v_1v_2+v_0v_1+v_0v_2}$