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A car moves from X to Y with a uniform s...

A car moves from `X` to `Y` with a uniform speed `v_u` and returns to `X` with a uniform speed `v_d`. The average speed for this round trip is :
(a) `(2v_(d)v_(u))/(v_(d)+v_(u))` (b) `sqrt(v_(u)u_(d))` (c) `(v_(d)v_(u))/(v_(d)+v_(u))` (d) `(v_(u)+v_(d))/(2)`

Text Solution

Verified by Experts

We know that, average speed `=("Distance travelled")/("Time taken")`
Let `t_(1)` and `t_(2)` be times by the car to ge from X to Y and then from Y to X, respectively.
Then, `t_(1)+t_(2)=(XY)/(v_(u))+(XY)/(v_(d))=XY((v_(u)+v_(d))/(v_(u)v_(d)))`
Total distance travelled `= XY+XY=2XY`
Therefore, average speed of the car for this round trip is
`v_(av)=(2XY)/(XY((v_(u)+v_(d))/(v_(u)v_(d))))` or `v_(av)=(2v_(u)v_(d))/(v_(u)+v_(d))`
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