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A self-propelled vehicle of mass m, whos...

A self-propelled vehicle of mass m, whose engine delivers a constant power P, has an acceleration `a = (P//mv)`. (Assume that there is no friction). In order to increase its velocity from `v_(1)` to `v_(2)`, the distan~e it has to travel will be:

A

`(m)/(3p)(V_(2)^(1)-V_(1)^(3))`

B

`(3p)/(m) (v_(2)^(2)-V_(1)^(2)`

C

`(m)/(3p)(V_(1)^(2)-V_(1))`

D

`(m)/(3p) (V_(1)^(2)-V_(1))`

Text Solution

Verified by Experts

The correct Answer is:
A
`a=(P)/(mv)` or `(dv)/(dt)`= `(P)/(mv)` or `(dv)/(ds)((dt)/(dt))= (P)/(mv)`
or `v(dv)/(ds) = 9p)/(mv)` or `v^(2dv= (P)/(m)ds`
Hence `int_(v_(1))^(v_(2))V^(2)dv=(P)/(m)int_(0)^(s)ds`
or `(V^(3)/(3)I_(V-(1))^(V-(2))`=(P)/(m)s`
`therefore s= (m)/(3p) (V_(2)^(3)-V_(1)^(2=3))`
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