Question

A car of mass m starts from rest and accelerates
so that the instantaneous power delivered to the
car has a constant magnitude Po: The
instantaneous velocity of this car is proportional to​

Answer 1

Answer:

$v\propto t^{1/2}$

Explanation:

Given

Instantaneous power has constant magnitude $P_0$

We know that

Power = Force × Velocity

$P_0=F.v$

$P_0=(ma).v$

$P_0=(m\frac{dv}{dt}).v$

$\implies P_0dt=mvdv$

$\implies \int P_0dt=m\int vdv$

$\implies P_0t=m\frac{v^2}{2}$

$\implies v\propto t^{1/2}$

Hope this helps.

Answer 2

Given:

Mass of car = m

initial velocity =0

Instantaneous power delivered to car = P₀

Formula Used:

Power = Force × velocity

Calculations:

$P_o=Fv\\P_o=(ma)v\\a=\frac{dv}{dt}\\P_o=(m\frac{dv}{dt})v\\P_odt=mvdv$

Integrating:

$P_ot=\frac{mv^2}{2}\\v=\sqrt{\frac{2P_ot}{m}}\\v\propto t^{\frac{1}{2}}$

Learn more about: Force and power

brainly.in/question/1721323

brainly.in/question/16185022

#learnwithbrainly