# If a car is *accelerating* uphill, does it *gain* kinetic energy?

I had an exam yesterday on physics (9th Grade), there was a question that confused me a lot. It said: "If a Gas Car is accelerating uphill, what happens to its G.P.E and K.E?"

A: It loses potential energy and loses kinetic energy.

B: It loses potential energy and gains kinetic energy.

C: It gains potential energy and loses kinetic energy.

D: It gains potential energy and gains kinetic energy.

--I chose the answer D, because the car is accelerating so its definitely gaining more speed so it must gain kinetic energy too. The teacher said that it wasn't the right choice, C was. He didn't really explain why, I argued that it said that the car was "accelerating" and not "decelerating".

I could really use some help on this~!

• "He didn't really explain why." That's too bad because I'm pretty sure that your instructor is the only person you can ask who knows what actually was going on inside his head. Commented Dec 10, 2023 at 17:41
• Your reasoning about speed is correct. If the speed was increasing then the kinetic energy was increasing. Commented Dec 10, 2023 at 17:45
• Without any more context the answer D should be chosen, since "accelerating" (without any further context) would be taken to mean gaining speed in normal English usage. Further, the question indicates the car is a "gas car" meaning it could indeed be gaining speed while going uphill. Seems to me like you have a bad physics teacher, which is unfortunately not uncommon in high school.
– hft
Commented Dec 10, 2023 at 21:35
• This is a poorly worded question. Acceleration can be positive or negative. For positive acceleration, "D" is the correct answer. For negative acceleration, "C" is the correct answer. Perhaps you can get your teacher to omit this question when grading the test. Commented Dec 11, 2023 at 0:26
• How many of your fellow students also picked D? Because yes, this question is very badly written if the intended answer was C. If almost all of you picked D, that's a failing on the teacher's part, not yours Commented Dec 11, 2023 at 5:35

D is correct.

The teacher is mistaken.

Your teacher may be confused because of the concept of conservation of energy, which says that the total energy of an isolated system does not change. As a result, they might erroneously believe this means that the kinetic energy must decrease while going uphill, leading to picking answer C.

The flaw in this logic is that there are (at least) 5 relevant parts to understand the total energy here. You have:

• Gravitational Potential Energy. As the car moves uphill this increases.
• Linear Kinetic Energy, which is what you and your teacher disagree over.
• Rotational Kinetic Energy of the wheels. Assuming the car is not slipping, this will be proportional to the linear kinetic energy so it does not change the conceptual picture here.
• Chemical Potential Energy from the power source (gasoline or battery).
• Energy which will be lost to the environment due to e.g. drag and friction. Cars are not actually isolated systems (especially gas cars, which need to intake oxygen to burn fuel and exhaust the resulting fumes). This isn't important here but is needed for the accounting to work.

Because the chemical potential energy is always decreasing (that's what powers the motor to turn the wheels), there is no requirement that the linear kinetic energy decrease just because the car is moving uphill. If there were, it would be impossible to start a parked car going even slightly uphill.

As for the answer, under normal English conventions, I would usually take "accelerating uphill" to mean that the velocity and acceleration are both pointed uphill, meaning the speed (and therefore kinetic energy) is increasing. Therefore I would have picked the same answer D as you.

With that said, "accelerating uphill" is actually quite an ambiguous phrase. Could it mean just that the acceleration is pointed uphill and the velocity is actually downhill? For example "As the car rolls backward down the hill, the driver presses the pedal to accelerate upward". This could lead you to pick A. Or could it mean that the velocity is pointed uphill and the acceleration is actually downhill? We would more typically to this as "deceleration while going uphill" but it's not technically wrong to call it acceleration as well (just acceleration that happens to be backwards). That might lead to answer C being chosen. We need to know both the direction of the velocity and the acceleration here, and the phrasing of the question is imprecise enough that it is difficult to be certain of either of them. Only your teacher knows what they intended it to mean, but in my opinion your answer is the most reasonable one.

Since we don't know the sign of the acceleration, it's not answerable...other than either C or D; however, since (de)acceleration can be used to mean positive (negative) acceleration, D looks correct to me.

Edit: Note that the phrase "can be used to mean" is synonymous with common English and/or "strongly suggests", but this is a physics problem, and we all know physics and language don't always mix.

• Common English usage would imply the car is gaining speed Commented Dec 10, 2023 at 16:58
• "accelerating uphill" strongly suggests that the the acceleration vector is non-zero, and that it points toward the top of the hill. The velocity vector, on the other hand, is completely unspecified. If the car were headed, down the hill, then stepping on the brake would be "accelerating uphill," and the answer would be (A). Seems like answers (C) and (D) both require the velocity vector to point toward the top of the hill. The only way you get (C) then is if the car is moving toward the top of the hill, but accelerating in the opposite direction to its motion (i.e., "downhill"). Commented Dec 10, 2023 at 17:44