Direction of frictional force acting on car

[coreluccio]

I posted the solution to the problem I am having below. I did this problem and got it wrong because I had the force of friction on the car acting in the opposite sense (which I argue it should be). I don't get this at all, have they made a mistake in the solution? The wheels apply a backward force on the road and the road applies a forward reactive force on the wheels, so why would the friction on the car be acting backwards, unless the car is skidding, which it isn't in this question?

http://bigpichost.com/files/untitled_gdq49mdu.jpg

 

[rcgldr]

The wheels apply a backward force on the road and the road applies a forward reactive force on the wheels.

This is only true if the cars's rate of acceleration is greater than if it were coasting with only gravity accelerating it at point A on the hill. If cars rate of acceleration is slower than coasting, then the brakes are being applied to reduce the rate of acceleration.

You've already done most of the math, so at point A, if the car was coasting, what would it's rate of acceleration be?

 

[coreluccio]

This is only true if the cars's rate of acceleration is greater than if it were coasting with only gravity accelerating it at point A on the hill. If cars rate of acceleration is slower than coasting, then the brakes are being applied to reduce the rate of acceleration.

You've already done most of the math, so at point A, if the car was coasting, what would it's rate of acceleration be?

Ah you are right. I hadn't even considered that. The component of gravity in the tangential direction gives the car an acceleration of 4.39 m/s^2, so the car would need to be breaking to have a net 3 m/s^s acceleration. Thank you.