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Show that the speed v reached by a car of mass m that is driven with constant power P is given by v = (3xplm) 1/3 , where x is the distance traveled from rest.

Show that the speed v reached by a car of mass m that is driven with constant power
P is given by
                v = (3xplm)1/3,
where x is the distance traveled from rest.

Grade:12th pass

3 Answers

downey zer
73 Points
6 years ago
P=F.v
m(dv/dt)v=P
m(dv/ds)(ds/dt)v=P
m(dv/ds)v2=P
mv2dv=Pds
integrate by putting limits v=0 to v and s=0 to s=x
we get 
v=(3xP/m)1/3
hope that helps . please approve the answer if it did 
abcde
21 Points
5 years ago
If the power is constant then the force on the car is given by F = P=v. But the force isrelated to the acceleration by F = ma and to the speed by F = mdvdt for motion in one dimension.ThenF = P/vv;mdvdt= Pv;mdxdtdvdx= Pv;mvdvdx= Pv;Z v0mv2dv =Z x0Pdx;13mv3 = Px:We can rearrange this nal expression to get v as a function of x, v = (3xP=m)1=3:
Utkarsh shrivastav
13 Points
4 years ago
Very easily question , rbu not able to sooner it , if not, them don't prepare for iit  , focus on boards

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