Car of mass 1250kg travels up a straight hill of length 500m. Its height is 30m. The power of its engine is 30kw and is constant. Its acceleration is 4m/s² at the bottom and 0.2m/s² at the top of the hill. The resistive force is 1kn. Find the gain in KE of the car.

Absurd question right? Why The hell will acceleration decrease. The resultant force is constant. Car is not nearing terminal velocity as they said that the resistive force is 1kn. Then why?
If u think it is absurd, then say that u agree with me. If not, then tell why. Please.

Not absurd... ever drive a smaller car up a steep hill. Had the same power at the bottom as it has at the top... think about it, and why.

Not absurd, but for a different reason than Smoothy aluded to. Remember that you are told that power is constant in this problem, not force. Power is equal to the force of the motor times the velocity of the car, which means that for a car with constant HP the faster you go the less force the motor produces and the less acceleration you have (even if you totally discount wind resistance, as we do here). So its logical that rate of acceleration decreases with increasing velocity.

I suggest you start with sum of forces = ma, and use the fact that the force supplied by the engine is equal to its power divided by the velocity of the car. From this you can calculate the velocity at the bottom and at the top, and hence the increase in KE.

Wow! U have opened my eyes- really. Let me try now.
But what Is that resistive force? Does it include everything like friction , drag, component of weight ?

Glad to be of help. You have the resistive force of the 1 kN, I suppose due to friction. You also have the force of gravity resisting the car as it goes up the slope.

I thought that resistive includes component of weight. Because that is also a resistive force. So should pull of gravity be already included in that 1kn ?

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Originally Posted by Yusf

I thought that resistive includes component of weight. Because that is also a resistive force. So should pull of gravity be already included in that 1kn ?

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I don't know. Is there a diagram that may give a clue as to whether the "resistive force" includes the car's weight on the incline?

There isn't any diagram. I found the question in a revision book- which doesn't have answers too.
Kindly tell me what do u think (and y). I will consider that final.

Adding in the effect of gravity on the incline as an additional resistive force is just a detail, and doesn't really add anything with respect to the learning process. The main point of the problem was to understand the relation of power, force, and acceleration, so I would just use the resistive force you're been given and leave it at that.

So, what did you get for an answer - what is the change in KE?