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A car drives along the straight level frictionless road by an engine delivering constant power. How is velocity of the car related to time elapsed?

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Power is given by f.vwhere f is force and v is velocity of particle power =kmav=km(dv/dt)v=kmdv x v= kdtintegrating both sides mv^2=ktv is directly proportional to√t
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Power =Force*Velocity Power=Const Now multiply 't' both sides So power*time=Energy Const*t=m.a.v.t Const *t=m.dv/dt.(v).t Now by rearrangement Const/m*(dt)=vdv Now integ both sides Const/m*(t)=v^2/2 Therefore V= const *root (t) :)
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Power =Force*Velocity 

Power=Const

Now multiply 't' both sides

So power*time=Energy

Const*t=m.a.v.t

Const *t=m.dv/dt.(v).t

Now by rearrangement 

Const/m*(dt)=vdv

Now integ both sides

Const/m*(t)=v^2/2

Therefore

V= const *root (t)

:)

 

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