Calculating Max Velocity of 2 Tonne Car: 60kW Power

[Bucky]

"A car of mass 2 tonnes has an engine that can generate 60kW of power. Determine its maximum velocity in m/s along a level road that has a coefficient of friction 1/2"

well I am quite lost. i know:-

power is force times velocity...and force is mass times acceleration...but I am not sure how to apply these.

since its the maximum velocity the force applied would 'cancel out' the force of the friction so there would be no increase in speed.

but to be honest I am really not sure where to go from here.

 

[whozum]

The friction force is independent of the force applied. You can find the magnitude of the friction force with the given information.

After that, I don't know though.

 

[z0r]

I suppose that's the kinetic coefficient of friction... in that case, we know that the kinetic frictional force will be:

$$F = \mu_k N$$, where mu is the kinetic coefficient of friction and N is the normal force (the mass of the vehicle times gravitational acceleration).

Now, we know something stops accelerating when the forces on it add up to zero... so it will be a matter of saying that the maximum velocity has been reached when the car's tires are pushing ahead as much as the road is pushing back.

 

[ek]

$$F_f = \mu_k N$$

$$F_c = P/v$$

$$F_f = F_c$$ (at max velocity)

$$v = P/\mu_kmg$$

In SI units, remember.