Power delivered to wheels of car with constant air resistance

[I_Try_Math]

Homework Statement

Suppose that the air resistance a car encounters is independent of its speed. When the car travels at 15 m/s, its engine delivers 20 hp to its wheels. (a) What is the power delivered to the wheels when the car travels at 30 m/s? (b) How much energy does the car use in covering 10 km at 15 m/s? At 30 m/s? Assume that the engine is 25% efficient. (c) Answer the same questions if the force of air resistance is proportional to the speed of the automobile. (d) What do these results, plus your experience with gasoline consumption, tell you about air resistance?

Relevant Equations

##KE=\frac 1 2 mv^2##
##P=\frac W t##

For part (a) the answer key is saying it's 40 hp. I'm having trouble understanding this. So the car accelerates to 15 m/s, then it stays at that velocity of 15 m/s, needing only 20 hp power to overcome the work done by air resistance. Supposing the car then accelerates to 30 m/s and stays at that velocity and given that air resistant is constant in this problem, wouldn't the engine only need that same 20 hp to overcome air resistance and keep the car at 30 m/s?

 

[jbriggs444]

For part (a) the answer key is saying it's 40 hp. I'm having trouble understanding this. So the car accelerates to 15 m/s, then it stays at that velocity of 15 m/s, needing only 20 hp power to overcome the work done by air resistance.
Supposing the car then accelerates to 30 m/s and stays at that velocity and given that air resistant is constant in this problem, wouldn't the engine only need that same 20 hp to overcome air resistance and keep the car at 30 m/s?

How far does the car travel in one second at 15 m/s?
How far does the car travel in one second at 30 m/s?

Say that the force of air resistance is ##F##.

How much work is done by air resistance against the car as it covers the distance for 15 m/s?
How much work is done by air resistance against the car as it covers the distance for 30 m/s?

Or...

Is the engine in first gear or second gear for the two situations? What does that mean for how much torque the engine has to provide in the two situations?

 

[Delta2]

##P=Fv##, apply this formula for the force of air resistance which is constant independent of speed and for the velocities ##v_1=15,v_2=30##.

 

[I_Try_Math]

How far does the car travel in one second at 15 m/s?
How far does the car travel in one second at 30 m/s?

Say that the force of air resistance is ##F##.

How much work is done by air resistance against the car as it covers the distance for 15 m/s?
How much work is done by air resistance against the car as it covers the distance for 30 m/s?

Or...

Is the engine in first gear or second gear for the two situations? What does that mean for how much torque the engine has to provide in the two situations?

Ah that makes it clear as day, thanks.