Question

A car's engine can deliver $90kW$ of power. The car's mass is $1000kg$.
Assume the total resistive force is proportional to the velocity: $|F_{friction}|=\alpha v$. The drag coefficient $\alpha$ is $\alpha =100Ns/m$. Car can maintain on a level road a maximum speed of _________ m/s?

Answer 1

As we know that $P=v{F}_{friction}$, we find $P=\alpha v^2$ or

$v=\sqrt{\frac{P}{\alpha }}=\sqrt{\frac{90000}{100}}=30m/s$

So, Required speed is , $v=30m/s$