A particle moves in a straight line from `A` to `B`
(a) for the first half of distance with speed `v_(1)` and the next half of distance with speed `v_(2)`.
(b) for the first one-third distance with speed `v_(1)` and the next two-third distance with speed `v_(2)`.
(c ) for the first one-fourth distance with speed `v_(0)`, the next half of distance with speed `2v_(0)` and the last one-fourth distance with speed `3v_(0)`.
Find the average speed in each case.

Options

A. `(v_(1)+v_(2))/2`
B. `sqrt(v_(1)v_(2))`
C. `(v_(1)v_(2))/(v_(1)+v_(2))`
D. `(2v_(1)v_(2))/(v_(1)+v_(2))`

Answer

D

Explanation

Let d be the distance.

Average speed`=d/((d//2)/v_(1)+(d//2)/v_(2))=(2v_(1)v_(2))/(v_(1)+v_(2))`