A car moves from `X` to `Y` with a uniform speed `v_u` and returns to `Y` with a uniform speed `v_d`. The average speed for this round trip is :

Options

A. 1) `frac(2V_(d)V_(u))(V_(d)+V_(u))`
B. 2) `sqrt(V_(u)V_(d))`
C. 3) `frac(V_(d)V_(u))(V_(d)+V_(u))`
D. 4) `frac(V_(d)+V_(u))(2)`

Answer

A

Explanation

We
`("Average speed")=frac(("Distance travelled"))(("Timetaken"))=frac(d)(1)`
Let `t_(1)` and `t_(2)` be times taken by the car to go from X There from Y to X respectively
Then,
`t_(1)+t_(2)=(frac(XY)(v_(u)))+(frac(XY)(v_(d)))=XY(frac(v_(u)+v_(d))(v_(u)v_(d)))`
Total distance travelled d
=XY+XY=2XY Therefore average spee of the car this round
covered by it trip is ``v_(av)=frac(2xy)(xy(frac(V_(u)+V_(d))(V_(u)V_(d))))or`
`V_(au)=frac(2v_(u)v_(d))(v_(u)+v_(d))`