Question

a car of mass m starts from rest and accelerates so that the instantaneous power

Answer 1

a car of mass M starts from rest and accelerates so that the instantaneous power _____ will be powerful or increased

Answer 2

Answer:

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

Explanation:

The question is:

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:​

Solution:

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.