What is instantaneous acceleration?

[parshyaa]

How their can be instantaneous acceleration, its impossible to have change in velocity at a particular position(instant), we can have velcoity or speed at a particular point but how can we have change in velocity at a particular instant?

 

[andrewkirk]

how can we have change in velocity at a particular instant

We don't.

Acceleration is simply the derivative of velocity with respect to time. Spend some time pondering the definition of derivative as a limit as $\delta t\to 0$, and how it applies to this particular case, and you'll see how it works.

 

[parshyaa]

We don't.

Acceleration is simply the derivative of velocity with respect to time. Spend some time pondering the definition of derivative as a limit as $\delta t\to 0$, and how it applies to this particular case, and you'll see how it works.

You mean Δt→0

 

[Ssnow]

Hi, from your velocity function $v(t)$ respect the time $t$ you can define the instantaneous acceleration in $t=t_{0}$ by the derivative:

$a(t_{0})=\lim_{\Delta t \rightarrow 0}\frac{v(t_{0}+\Delta t)-v(t_{0})}{\Delta t}$

Ssnow

 

[andrewkirk]

You mean Δt→0

No I don't.

 

[parshyaa]

Forget about definition, why we are making a definition, when we know that logically instantaneous acceleration is not expressible(how there can be a change in velocity at a particular position). From
$a(t_{0})=\lim_{\Delta t \rightarrow 0}\frac{v(t_{0}+\Delta t)-v(t_{0})}{\Delta t}$
As $\Delta t\rightarrow 0$
$a(t_{0})=\frac{\delta v}{\delta t}$
As time period is too small we say that its the instantaneous acceleration, but still it represents the change in velcoity at an instant( simillarly v= dr/dt(v&r are vector) it represents the velocity at an instant)

@Ssnow

 

[parshyaa]

I think we defined instantaneous acceleration mainly to use its vector property so that we can determine in which direction velcoity is increasing and its magnitude will be the change in velocity at a very small interval(and we say it as change in velocity at an instant or acceleration at an instant), therefore we never use scalar version or we didn't defined scalar version of acceleration.
Its just my attempt to answer this question.

 

[jbriggs444]

If we can define instantaneous velocity as the instantaneous rate of change of position with respect to time then how is it problematic to define instantaneous acceleration as the instantaneous rate of change of velocity with respect to time?

 

[Ben Wilson]

I think we defined instantaneous acceleration mainly to use its vector property so that we can determine in which direction velcoity is increasing and its magnitude will be the change in velocity at a very small interval(and we say it as change in velocity at an instant or acceleration at an instant), therefore we never use scalar version or we didn't defined scalar version of acceleration.
Its just my attempt to answer this question.

when you first get in your car, a=0. You turn the key, a=0. You start to move, a=10 (pick any unit you want) then a few seconds later now the wheels are going faster a=40, then the wheels can't really go any faster so a=20, and at top speed when you can't get any faster a=0. It's useful to measure acceleration as an average, e.g. from start to a top speed of 60mph, we might say the car went from 0 to 60 in so many seconds. But when breaking down the motion into separate instances, we have different accelerations. This is the concept of instantaneous acceleration, i.e. the acceleration at this or that moment, as opposed to an average acceleration.

 

[parshyaa]

If we can define instantaneous velocity as the instantaneous rate of change of position with respect to time then how is it problematic to define instantaneous acceleration as the instantaneous rate of change of velocity with respect to time?

So the final definition becomes,

1. instantaneous velcity is the velocity of the particle at an instant{its completely logical because we can find the velcity of a particle at a particular instant(time)}
2. Instantaneous acceleration is the rate of change of velcity of a particle at a particular instant(this is not logical to me, how can we have change in velcoity at a particular instant)

As you said that what's the problem in defining this way, i didn't said that we can't define acceleration as rate of change of velocity(i think this definition is good for average acceleration but not for instantaneous acceleration as for above reasons)

 

[Ben Wilson]

when you first get in your car, a=0. You turn the key, a=0. You start to move, a=10 (pick any unit you want) then a few seconds later now the wheels are going faster a=40, then the wheels can't really go any faster so a=20, and at top speed when you can't get any faster a=0. It's useful to measure acceleration as an average, e.g. from start to a top speed of 60mph, we might say the car went from 0 to 60 in so many seconds. But when breaking down the motion into separate instances, we have different accelerations. This is the concept of instantaneous acceleration, i.e. the acceleration at this or that moment, as opposed to an average acceleration.

thats the simple physics definition. If you then have an issue with the math... v=dx/dt, a=dv/dt, they are the same mathematical objects: a derivative w.r.t a variable t; where x, v, and a are the vector quantities displacement, velocity and acc respectively.

 

[Ben Wilson]

So the final definition becomes,

1. instantaneous velcity is the velocity of the particle at an instant{its completely logical because we can find the velcity of a particle at a particular instant(time)}
2. Instantaneous acceleration is the rate of change of velcity of a particle at a particular instant(this is not logical to me, how can we have change in velcoity at a particular instant)

As you said that what's the problem in defining this way, i didn't said that we can't define acceleration as rate of change of velocity(i think this definition is good for average acceleration but not for instantaneous acceleration as for above reasons)

If you replace in 2. "rate of change of velocity of a particle" with "acceleration" .OR. replace in 1. "velocity of" with "rate of change of displacement of". Do you still have the same conceptual problem?

 

[A.T.]

Instantaneous acceleration is the rate of change of velcity of a particle at a particular instant(this is not logical to me, how can we have change in velcoity at a particular instant)

Note how the red part is missing in your question.

Seems like your problem is with math, not with physics:
https://en.wikipedia.org/wiki/Differential_calculus

And your logic makes no sense to me. Acceleration is a derivative of velocity, just like velocity is a derivative of position. Both have a instantaneous value at every time point.

 

[parshyaa]

Both have a instantaneous value at every time point.

How can we have a change in velcity at an instant(or acceleration at an instant)

 

[A.T.]

How can we have a change in velcity at an instant(or acceleration at an instant)

See post #13 again, I edited it.

 

[parshyaa]

See post #13 again, I edited it.

Do you mean that accelaration is the velocity at a instant of time and velocity is the position of a particle at a instant of time.

 

[Ben Wilson]

How can we have a change in velcity at an instant(or acceleration at an instant)

same way you can have change in position at an instant.

Do you mean that accelaration is the velocity at a instant of time and velocity is the position of a particle at a instant of time.

no. you need to learn calculus, which will define what an instantaneous rate of change is.

 

[jbriggs444]

So the final definition becomes,

1. instantaneous velcity is the velocity of the particle at an instant{its completely logical because we can find the velcity of a particle at a particular instant(time)}

How, experimentally, will you find the velocity of a particle at a particular instant?

Mathematically, we can define it -- no problem.

 

[parshyaa]

How, experimentally, will you find the velocity of a particle at a particular instant?

Mathematically, we can define it -- no problem.

By drawing a tangent at that instant

 

[Ben Wilson]

By drawing a tangent at that instant

impossible

 

[parshyaa]

By drawing a tangent at that instant

Okk i got it, we can't find velocity at a particular instant experimentally therefore we use calculus, what's the point.

 

[Ben Wilson]

Okk i got it, we can't find velocity at a particular instant experimentally therefore we use calculus, what's the point.

that dv/dt and dx/dt are the same things mathematically, so what is your problem with them behaving the same?

 

[parshyaa]

that dv/dt and dx/dt are the same things mathematically, so what is your problem with them behaving the same?

Actually my definition of accelaration was wrong, i always thaught that accelaration is the change in velocity w.r.t time,but correct definition is the ability to gain velocity is called acceleration, and therefore we can have acceleration at an instant, sorry for creating mess. Thank you so much

 

[Ben Wilson]

i always thaught that accelaration is the change in velocity w.r.t time so much

that is true... a=dv/dt

 

[parshyaa]

that is true... a=dv/dt

Yep both definitions are corrrct but the 2nd definition which i found on google explains completely that we can have accelaration at an instant.Accelaration is the change in velcoity w.r.t time but here change must be positive or velcity must increase. Therefore we can define instantaneous acceleration as the ability to increase its speed or gain its speed at an instant

 

[Dale]

• instantaneous velcity is the velocity of the particle at an instant{its completely logical because we can find the velcity of a particle at a particular instant(time)}

• Instantaneous acceleration is the rate of change of velcity of a particle at a particular instant(this is not logical to me, how can we have change in velcoity at a particular instant)

You are contradicting yourself here. Velocity is instantaneous rate of change in position. Acceleration is instantaneous rate of change in velocity. You cannot claim that instantaneous rates of change are OK for defining velocity but not ok for defining acceleration

 

[russ_watters]

This was pointed out but then appeared missed, so I'll point it out again:

Instantaneous acceleration is the rate of change of velcity of a particle at a particular instant(this is not logical to me, how can we have change in velcoity at a particular instant)

You stated it correctly, then re-stated it incorrectly! Acceleration is the rate of change of velocity. It almost sounds like you are trying to incorrectly envision it as a step change.

 

[sophiecentaur]

Do you mean that accelaration is the velocity at a instant of time and velocity is the position of a particle at a instant of time.

Try reading this wiki link. The basic concepts of calculus are not intuitive and your questions / challenges are dealt with, afaics, in here - if you read it all.

 

[parshyaa]

Instantaneous velocity: its the velocity of an object at a particular instant/moment of time.
mathematically: Its the rate of change of displacement/position of an object w.r.t time.
Instantaneous acceleration: its the acceleration of an object at a particular instant/moment of time.
Mathematically: its the rate of change of velocity w.r.t time.
Suppose i am applying force continuously on an object, then object accelerates, and then somebudy asked what is the acceleration of that object when time was 4 second, therefore introduction of instantaneous acceleration is must.
Thank you

 

[A.T.]

Instantaneous velocity: its the velocity of an object at a particular instant/moment of time.
mathematically: Its the rate of change of displacement/position of an object w.r.t time.
Instantaneous acceleration: its the acceleration of an object at a particular instant/moment of time.
Mathematically: its the rate of change of velocity w.r.t time.

Right, so if you understand instantaneous velocity, then what is your problem with Instantaneous acceleration? Both are derivatives w.r.t time.

So my question is how we can have ...

We cannot help you, if you just keep repeating "How can it be..." without explaining what your problem with it is.

 

[parshyaa]

Right, so if you understand instantaneous velocity, then what is your problem with Instantaneous acceleration? Both are derivatives w.r.t time.We cannot help you, if you just keep repeating "How can it be..." without explaining what your problem with it is.

I just edited my post

 

[A.T.]

Suppose i am applying force continuously on an object, then object accelerates, and then somebudy asked what is the acceleration of that object when time was 4 second

a = F / m

 

[parshyaa]

a = F / m

Yes but i just gave that example to explain the importance of instantaneous acceleration, finally acceleration is the ratio of velocity w.r.t time , therefore it can occur at a particular instant of time.

 

[A.T.]

Yes but i just gave that example to explain the importance of instantaneous acceleration,

Then you should add that the force or mass varies with time. Otherwise instantaneous acceleration equals average acceleration.

 

[parshyaa]

Then you should add that the force or mass varies with time. Otherwise instantaneous acceleration equals average acceleration.

Yes, i meant the same.

 

[Dale]

finally acceleration is the ratio of velocity w.r.t time

Acceleration is the derivative of velocity wrt time.

therefore it can occur at a particular instant of time

It sounds like you now agree that instantaneous acceleration is meaningful, just like instantaneous velocity.

 

[parshyaa]

Instantaneous velocity: its the velocity of an object at a particular instant/moment of time.
mathematically: Its the rate of change of displacement/position of an object w.r.t time.
Instantaneous acceleration: its the acceleration of an object at a particular instant/moment of time.
Mathematically: its the rate of change of velocity w.r.t time.
Suppose i am applying force continuously on an object, then object accelerates, and then somebudy asked what is the acceleration of that object when time was 4 second, therefore introduction of instantaneous acceleration is must.
Thank you

@Dale

 

[russ_watters]

@Dale

You didn't ask any questions, but all of those statements look fine.

 

[parshyaa]

You didn't ask any questions, but all of those statements look fine.

Yes,becuase my doubt is clear now, thanks to all of you

 

[rumborak]

On a related side note, there is something called "jerk" in physics, which is the derivative of the acceleration over time:

https://en.m.wikipedia.org/wiki/Jerk_(physics)

 

[sophiecentaur]

On a related side note, there is something called "jerk" in physics, which is the derivative of the acceleration over time:

https://en.m.wikipedia.org/wiki/Jerk_(physics)

And the jerk is what actually happens in pretty well every mechanical occurrence . Put your foot down on a car accelerator and you will find the force on your back varies with time. (Like when the turbo kicks in. You can't use the SUVAT equations with motor cars because the acceleration is not uniform at all.
Edit: When I first was taught SUVAT in School, I missed the word "uniform" in "uniform acceleration'. That looking out of the window incident accounted for a lot of initial problems with comprehension. I wish I had learned that lesson because I have been nodding off regularly at vital moments ever since.

 

[LLT71]

like a lot of people out there that paradoxical thing bugged me since high school, but no one ever seemed to explain me better than this guy:



OP I strongly advise you to watch this video to really get a clear(er) picture of a derivative.

 

[Vidujith Vithanage]

The video posted by LLT71 is interesting, " Instantaneous rate of change" is explained clearly in that. Simply it is the rate of change occurs during a very small duration of time, when we take the derivative we allow the time difference to approach zero,

 

[sophiecentaur]

The video posted by LLT71 is interesting, " Instantaneous rate of change" is explained clearly in that. Simply it is the rate of change occurs during a very small duration of time, when we take the derivative we allow the time difference to approach zero,

He deals with the apparent problem quite well but he doesn't really needs go to all that trouble. If you are prepared to use Maths as the primary way of explaining this sort of process and only use hand waving as a secondary medium, there never would be a problem. This is all down to Mathsphobia, imo.