If a body travels half the distance with velocity `v_(1)` and next half with velocity `v_(2),` then which one of the following will be the average velocity of the body?

Options

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

Answer

D

Explanation

Let the total distance covered by the body be S. Then time taken to cover half the distance with velocity `v_(1)` is
`t_(1)=((S//2))/(v_(1))=(S)/(2v_(1))`
Also, time taken to cover next half distance with velocity `v_(2)` is
`t_(2)=((S//2))/(v_(2))=(S)/(2v_(2))`
Now,
`"Average velcoity "=("Total distance")/("Total time taken")=(S)/(t_(1)+t_(2))`
`=(S)/((S)/(2v_(1))+(S)/(2v_(2)))=(2)/((1)/(v_(1))+(1)/(v_(2)))=(2v_(1)v_(2))/(v_(1)+v_(2))`