Power Calculation for a Car Driving on a Hilly Road with a Given Slope

[LauraMorrison]

Homework Statement

A car of mass 850 kg is driven at a steady speed of 70 km/hr up a hilly road
with a slope of 30°. Using the macroscopic energy equation, determine the
power delivered by the engine of the car.

Homework Equations

E= KE + PE
E = (1/2)mC^(2) + mgz
Power = E/t

The Attempt at a Solution

My attempt at a solution was:
E = 1/2mC^(2) + mg(Ctsin(30))
E = 1/2(850)(19.44)^(2) + (850)(9.81)(19.44)tsin(30)

Therefore

Power = (1/2(850)(19.44)^(2))/t + (850)(9.81)(19.44)sin(30)

Why do I still have an unknown t? I am supposed to be able to solve it with the information given but I can't get it!
Please please help!

 

[DrClaude]

Your problem is with

Power = E/t

You should be considering variations...

 

[LauraMorrison]

Do you mean the variations in potential and kinetic energy as the car drives up the hill? I am not sure how to calculate that, would you be able to explain?

I am sorry, I know it is such a simple question.

 

[DrClaude]

If you write $P = E/t$, think what happens if the car is going at constant speed on a flat road.

The power is used to change the energy of the car, so you have to consider $P = \Delta E / \Delta t$ or, even better, the instantaneous power $P = dE / dt$.

Hope this helps. Don't hesitate with further questions if it doesn't!