Question

Example 6. A body travelling along a straight line traversed one-half of the total distance with a velocity 0. The remaining part of the distance was covered with a velocity v, for half the time and with velocity vn for the other half of time. Find the mean velocity averaged over the whole time of motion.

I know The answer but i want the explanation why and how this question has to be done.​

Answer 1

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Let the total distance be d and time taken be t

Hence, for first half distance, time taken (t1) = d/2V0

Time left = t - t1 = t - d/2V0

Hence, distance travelled with v1 velocity = (t-d/2V0)/2 * v1

distance travelled with v2 velocity = (t-d/2V0)/2 * v2

Also, distance travelled with v1 velocity + v2 velocity = d/2

(t-d/2V0)/2 * v1 + (t-d/2V0)/2 * v2 = d/2

tv1 + tv2 = d/2 *(1+v1/v0 + v2/v0)

d/t = (v1+v2)*v0/2(v0+v1+v2)

Also, mean velocity = d/t

mean velocity = (v1+v2)*v0/2(v0+v1+v2)