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

Answer

C

Explanation

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