In what type of motion is the average acceleration equal to the instantaneous acceleration?

Question

please do explain well, for me to understand too.

thank you.

Answer 1

In a uniformly accelerated motion, acceleration (and thus the sum of forces applied to the object of interest) is constant. In that case, the instantaneous acceleration is equal to the average one.
A free fall (in vacuum) is a uniformly accelerated motion.

Answer 2

Acceleration is the result of a force being applied to an object. For the instantaneous acceleration to be the same as the average acceleration, you would have to sustain the same amount of force on the object constantly for the recorded period of time, while making sure that there were no opposing forces varying the acceleration through friction or anything like that.

The only situations in which I can imagine actually causing this type of situation would be in a vacuum such as space. For example, if an object were to be placed in space far enough away from everything that no gravitational bodies such as planets or stars could affect it, and turned on a rocket that gave produced the same amount of force over an extended period of time, the object would be constantly accelerating at the same speed, and therefore would have the same instantaneous acceleration as average acceleration.

The only problem is that technically that would not even work, because the object would change mass as it used up fuel, so the acceleration would gradually change. It also does not quite work to have the force source be the gravity of a planet or star, because the force of gravity changes as the object nears the gravitational body.

In conclusion it is technically not even realistically possible, but it could be approximated closely enough through electronically controlled burning of fuel that the error would not matter.

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On second thought an object has the same instantaneous acceleration as its average acceleration if it is not accelerating.

This could be accomplished by moving the object at a constant speed in a constant direction, or by keeping the object still.

Answer 3

If the acceleration is constant, the instantaneous acceleration at any point in time is equal to the average acceleration.

A graph of the acceleration vs. time would look like a flat, horizontal line.

Answer 4

At any instant of time, an object or particle can be at a definite [fixed] point at a particular instant of time.

When there is change in acceleration,

At a particular point on the path of the object the acceleration can vary with time.

Or

At a particular instant of time, the acceleration at various points on its path can vary.

Therefore, there are two average accelerations.

One is the average acceleration along the entire path (or between two points) at a particular instant of time.

The other is the average acceleration during an interval of time (or between two instants of time) at a particular point on the path.

Instantaneous acceleration is the acceleration at a particular point at an instant of time.

If the acceleration is constant, whether it is between two points or between two interval of time, the question of average do not rise, since there is no change in acceleration.

With out much explanation, we can use either average or constant acceleration, if there is no change in the acceleration.

Your question is

In what type of motion is the average acceleration equal to the instantaneous acceleration?

As already stated the question of average arises only when there is variation in accelerations, (in fact in any quantity).

"The accelerations vary "implies," At every instant of time the instantaneous accelerations vary" or "At every point in a give interval of path, the instantaneous accelerations vary".

By definition of average, one of the instantaneous values of acceleration must coincide with the average value at a particular instant of time or at a particular point at one instant in all types of motions.

In a uniformly accelerated motion, the acceleration is a constant and the question of average acceleration does not arise.

Uniformly accelerated motion means the instantaneous accelerations are constant at any point and at any time.

Answer 5

when the acceleration is constant, that mean the rate of change of velocity is same, thus the average acceleration also same with instantaneous acceleration.

Answer 6

Motion in a constant accleration field. If the instantaneous accleration was ai(t), then the average accleration would be INT ai(t) dt /t
where INT indicates an integral, t is time, and the time goes from t1 to t2. Only if ai(t) is a constant will this be true.

Answer 7

average acceleration is from point a to point b

instaneous acceleration is taken at an instant somewhere or anywhere in between point a to point b

Answer 8

You have described the way light travels, it instantly reaches it's speed and continues on at the same speed through a vacuum.