A person travels along a straight road for the first half length with a constant speed `v_(1)` and the second half length with a constant speed `v_(2)`. The average speed V is:

Options

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

Answer

B

Explanation

Let `t_(1)` and `t_(2)` be time taken to cover first and second half length
Then `t_(1) = (x//2)/(v_(1)) = (x)/(2v_(1))`
`t_(2) = (x//2)/(v_(2)) = (x)/(2v_(2))`
`v_(av) = ((x//2 + x//2))/((x)/(2v_(1)) + (x)/(2v_(2))) = (1)/((1)/(2v_(1)) + (1)/(2v_(2)))`
`(1)/(2v_(1)) + (1)/(2v_(2)) = (1)/(v_(av))`
`(v_(1) + v_(2))/(2v_(1) v_(2)) = (1)/(v_(av))`
`v_(av) = (2v_(1)v_(2))/(v_(1) + v_(2))`