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. `(V_(1) + V_(2))/(V_(1)V_(2))`

Answer

c

Explanation

Time taken to travel a distance of L/2 with velocity `V_(1)` is .
`t_(2) = (L//2)/(V_(1))` and
Time taken to travel a remanining distance of L/2 with velocity `V_(2)` is
`t_(2) = (L//2)/(V_(2))`
Average velocity , `v_(av) = (L)/(t_(1) + t_(2)) = (L)/((L)/(2)[(1)/(V_(1)) + (1)/(V_(2))])`
` = (2V_(1)V_(2))/(V_(1) + V_(2))`.
The correct option is (c).