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Question

An auto travels the first half time with a uniform speed u and the next half time with a uniform speed v. Find its average speed.


A
2uv
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B
u+v2
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C
uv
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D
uv2
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Solution

The correct option is B u+v2

Given, speed of the auto during the first half of the journey is u and the next half of the journey is v
Let total time taken for the journey be T
Time taken for the first half of the journey be T2 and the next half of the journey be T2
Let the average speed be Vav
We know, speed=Distancetime
Distance=speed×time

During the first half of the journey, distance, d1=u×T2
During the second half of the journey, distance, d2=v×T2
Total distance =d=d1+d2
=u×T2+v×T2
d=T2(u+v)

Average speed,Vav = Total distanceTotal time taken
=dT
=T2(u+v)T
=u+v2


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