# Should not the acceleration acting on the stone being dropped be $a$ as well along with $g$?

the question is:

A stone is released from an elevator going up with an acceleration a. The acceleration of the stone after the release is

(a) a upward

(b) (g-a) upward

(c) (g-a) downward

(d) g downward.

my teacher told us that ans is (d). according to him As soon as the stone is released from the lift the acceleration 'a' of the lift has no effect on the stone, it is now only under the influence of the gravitational pull. So only acceleration due to gravity 'g' acts.

but according to me acceleration of the lift i.e 'a' should also be acting at the stone at the instant it is released. I got my logic from a question in which a hot air balloon is moving up with a constant velocity 'u' and a stone is released from the ballon on reaching a certain height. it asked what will be the velocity of the stone at the instant it is released from the hot air balloon and the answer was "u" velocity upwards.

although in one it is asking about acceleration and in other about velocity, I find both the question pretty similar. please correct me if wrong. please give me the difference between the two Questions .

You're confusing velocity with acceleration. The acceleration "a" acts on the stone only until you let go.

"After the release" means "after you let go", hence you no longer impart any acceleration to the stone, and "a", the acceleration of the lift, no longer affects the stone. In your balloon experiment, the stone has velocity "u", but in the lift the stone also has velocity "v" at the instant you let go. Just as in the balloon, as soon as you let go, gravity takes over and starts to act against "v" (or "u" in the balloon). The only difference is that, as your lift is accelerating, the stone's velocity is changing continuously with the lift - until you let go when the lift no longer affects it.

Your teacher is right. You are confused about acceleration and velocity, which can be tricky.

Acceleration is the change of velocity with respect to time and nothing can be accelerated without a force acting on it. Think about it. Your car won't drive unless the engine is powering it. Your bike won't go unless you pedal. So as soon as a force starts/stops acting on an object it will start/stop accelerating.

Everything on Earth is subject to its gravitational attraction. On the surface everything is accelerated towards Earth with the acceleration being equal to $$g$$. Throw a stone upwards. It will always experience the same acceleration downwards, but the velocity changes throughout.

Now to your elevator: the elevator's grip acts like a force pulling the stone upwards, so the overall acceleration of the stone is changed. Once the stone is released, the only force left is gravity, so the acceleration is back to $$g$$

So the answer should be given by taking a particular frame of reference....imagine if you are in the elevator, you will feel that the acceleration of the stone is g+a downwards but now imagine that you're on the ground looking at the stone falling, you will feel that the acceleration is simply g downwards hence I think that the answer was given taking ground as the reference

In the hot air balloon, for an observer at the ground the stone is moving up with velocity u so when you are releasing the stone, you are freeing it from any other force except gravity(neglecting air resistance) but the stone is already moving with velocity u upwards

It's all relative!! . I hope you understand