A person travels along a straight road f...

A person travels along a straight road for the first half length with a constant speed `v_(1)` and the second half length with a constant speed `v_(2)`. The average speed V is:

`(v_(1) + v_(2))//2`

`2v_(1) v_(2)//(v_(1) + v_(2))`

`(v_(1) v_(2))^(1//2)`

`(v_(2)//v_(1))^(1//2)`

Text Solution

Verified by Experts

The correct Answer is:

Let `t_(1)` and `t_(2)` be time taken to cover first and second half length
Then `t_(1) = (x//2)/(v_(1)) = (x)/(2v_(1))`
`t_(2) = (x//2)/(v_(2)) = (x)/(2v_(2))`
`v_(av) = ((x//2 + x//2))/((x)/(2v_(1)) + (x)/(2v_(2))) = (1)/((1)/(2v_(1)) + (1)/(2v_(2)))`
`(1)/(2v_(1)) + (1)/(2v_(2)) = (1)/(v_(av))`
`(v_(1) + v_(2))/(2v_(1) v_(2)) = (1)/(v_(av))`
`v_(av) = (2v_(1)v_(2))/(v_(1) + v_(2))`

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A bus covers the first half of a certain distance with speed v_(1) and the second half with a speed v_(2) .The average speed during the whole journey is :

`(v_(1)+v_(2))/(2)`

`(v_(1)v_(2))/(v_(1)+v_(2))`

`sqrt(v_(1)v_(2))`

`(2v_(1)v_(2))/(v_(1)+v_(2))`

A person travels along a straight road for the first (t)/(3) time with a speed v_(1) and for next (2t)/(3) time with a speed v_(2) . Then the mean speed v is given by

`v=(v_(1)+2v_(2))/(3)`

`(1)/(v)=(1)/(3v_(1))+(2)/(3v_(2))`

`v=(1)/(3)sqrt(2v_(1)v_(2))`

`v=sqrt((3v_(2))/(2v_(1)))`

If a body covers first half of its journey with uniform speed v_(1) and the second half of the journey with uniform speed v_(2) . Then the average speed is

`V_(1)+V_(2)`

`(2V_(1)V_(2))/(V_(1)+V_(2))`

`(V_(1)V_(2))/(V_(1)+V_(2))`

`V_(1)V_(2)`