A vehicle travels half the distance (L) with speed ` V_1` and the other half with speed ` V_2`, then its average speed is .

Options

A. `(upsilon_(1)+upsilon_(2))/(2)`
B. `(2upsilon_(1)+upsilon_(2))/(upsilon_(1)+upsilon_(2))`
C. `(2upsilon_(1)upsilon_(2))/(upsilon_(1)+upsilon_(2))`
D. `(L(upsilon_(1)+upsilon_(2)))/(upsilon_(1)upsilon_(2))`

Answer

C

Explanation

Time taken to travel first half distance `t_(1)=(l//2)/(upsilon_(1))=(l)/(2upsilon_(1))`
Time taken to travel second half distance `t_(2)=(l)/(2upsilon_(2))`
Total time = `t_(1)+t_(2)=(l)/(2upsilon_(1))+(l)/(2upsilon_(2))=(l)/(2)[(1)/(upsilon_(1))+(1)/(upsilon_(2))]`
We know that, `upsilon_(av)` = Average speed
`=("total distance")/("total time")=(l)/((1)/(2)[(1)/(v_(1))+(1)/(v_(2))])=(2upsilon_(1)upsilon_(2))/(upsilon_(1)+upsilon_(2))`