What is the Significance of Instantaneous Acceleration in Classical Physics?

[Rahul Manavalan]

i understand why acceleration has much significance in Classical physics.
But something that has intrigued me is why my lessons focus a great deal on instantaneous acceleration.
I have had quite a hard time in figuring out what the practical application of this concept is!
Help me out guys!

 

[Chandra Prayaga]

Were you not equally worried with instantaneous velocity?

 

[Dale]

Any time that the acceleration occurs over a time scale that is smaller than what you are interested in you would probably approximate it as instantaneous. For example, if you are calculating the motion of a bunch of billiard balls, the time of each collision is so brief you would probably treat it as instantaneous.

 

[ZapperZ]

i understand why acceleration has much significance in Classical physics.

Actually, it doesn't!

You may think it does at the level you are learning basic kinematics, but go a bit further, and you won't hear the word "acceleration" utter that regularly anymore. You will hear more on "equation of motion" and "energy", etc., but very seldom on acceleration.

But something that has intrigued me is why my lessons focus a great deal on instantaneous acceleration.
I have had quite a hard time in figuring out what the practical application of this concept is!
Help me out guys!

As someone has asked you, about about instantaneous velocity? Do you also have a hard time figuring out the "practical application" of that as well?

You need to understand that when we first teach students basic mechanics, we can't use real world, "practical application"-type scenarios. That is just way too complicated! So we use idealized cases, in which you can learn HOW these physics concepts are applied without being distracted by the difficult mathematics.

Zz.

 

[Doc Al]

But something that has intrigued me is why my lessons focus a great deal on instantaneous acceleration.

When an object moves around--speeding up, slowing down, changing directions--at any given moment, the object has an instantaneous position, velocity, and acceleration. These may change from moment to moment. That's usually what is meant by instantaneous acceleration ($dv/dt$) in contrast to average acceleration ($\Delta v/ \Delta t$).

Or do you mean an "instantaneous" change in velocity, as others have supposed. (I suspect that's what you mean, but it can't hurt to make sure.) As explained, that's a useful approximation to make analysis easier.

 

[Dale]

Hmm, yes. I assumed that instantaneous acceleration referred to an acceleration which leads to a finite change in velocity over an instant of time. Everyone else seems to think that you are referring to the acceleration as a function of time, evaluated at an instant.

 

[sophiecentaur]

"Instantaneous Position" is a reasonable concept (we can accept that idea). After all, when something is moving, it is 'instantaneously' at every point along its path. At each position it will be traveling at a particular (perhaps ever changing) velocity and, if the Forces on it are also varying with position or time, then the acceleration can also be constantly varying. Each of those quantities - position, velocity and acceleration can have 'instantaneous' values at any given point in the motion. It doesn't need to end there. The rate of change of acceleration (or even the rate of change of the rate of change of acceleration) can also have instantaneous values at any position or time. Differential Calculus is all about that stuff.

 

[IgorIGP]

Rahul Manavalan as far as you

understand why acceleration has much significance in Classical physics.

you have to understand:

a great deal on instantaneous acceleration

Physics began as the science of interactions. The force as a quantitative characteristic (value) of the action is determined by the acceleration as its result. Newton is father of classical physics and his laws are basic and fundamental things. The first law equates rest and uniform motion as a constant mechanical state. Furthermore it establishes a direct link between that state presence and the absence of external action.
The second law defines a change of the mechanical state as the acceleration relative to inertial systems. In addition it offers to measure the force acting on the one unit (kilogram) of body's mass by the body's acceleration achieved as a result of this force action.
The concept of action was quite blurry before the introduction of these laws. In the doctrine Aristotle was established a link between the presence of the action as a cause and the presence of movement as a consequence. In addition that was wrong link. That is the concept of force is a fundamental concept of physics and acceleration accuracy limits the accuracy of the force. That is why the second law validity is determined by the acceleration accuracy (technically achievable of course). The instantaneous acceleration is the ideal abstraction of absolutely accurate acceleration. Thus, physics can not exist as a science without the instantaneous acceleration. The rest is mathematics, without which any area of knowledge is shamanism.