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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.


Options:
A .   u+v2
B .   uv2
C .   2uv
D .   uv
Answer: Option A
:
A

An Auto Travels The First Half Time With A Uniform Speed U A...           


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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