Question

a point moving on a straight line 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.

Answer 1

do + d1 +d2 = d
do = d/2
d1+d2 = d/2

to + t1 + t2 = t
to = do/Vo = d/2Vo

t2 = t1
t1 = d1/V1
t2 = d2/V2
so
d1/V1 =d2/V2
d2 = d1 V2/V1
so
t = d/2Vo + d1/V1 + d2/V2
average speed = d/t
= d / (d/2Vo + d1/V1 + d2/V2)
or
d/(d/2Vo + 2 d1/V1)

Answer 2

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