Understanding Acceleration Formulas: Instantaneous vs Average

[stephenranger]

Homework Statement

This is not a homework, just my understanding problem.

Homework Equations

We know that average acceleration can be calculated by: a_av=Δs/Δt
Is this formula also correct: a_av=0.5(a_fi+a_in) ??

One more question is: in the formulas: s = v₀t + 0.5at² and v_fi = v_in + at and (v_fi)² - (v_in)² = 2as

a in these equations is instantaneous acceleration or average acceleration ?

The Attempt at a Solution

 

[Chestermiller]

Homework Statement

This is not a homework, just my understanding problem.

Homework Equations

We know that average acceleration can be calculated by: a_av=Δs/Δt
Is this formula also correct: a_av=0.5(a_fi+a_in) ??

The first equation is never correct, since it doesn't even have the right units. The second equation is correct only if the acceleration is varying linearly with time.

One more question is: in the formulas: s = v₀t + 0.5at² and v_fi = v_in + at and (v_fi)² - (v_in)² = 2as

a in these equations is instantaneous acceleration or average acceleration ?

Both. These equations assume that the acceleration is constant, so it is both the instantaneous acceleration and the average acceleration.

Chet

 

[SammyS]

...

We know that average acceleration can be calculated by: a_av=Δs/Δt

A correct statement is: a_av=Δv/Δt .
Perhaps you had a typo.

Also true is v_av=Δs/Δt .

 

[stephenranger]

A correct statement is: a_av=Δv/Δt .
Perhaps you had a typo.

Also true is v_av=Δs/Δt .

Yes. I have a typo, sorry.

What's about this:

s = v0t + 0.5at2 and vfi = vin + at and (vfi)2 - (vin)2 = 2as

the acceleration "a" in these equations is instantaneous or average acceleration or both like Chestermiller said ?

 

[stephenranger]

The second equation is correct only if the acceleration is varying linearly with time.

Yes sir. if the acceleration is varying linearly with time, that means that it's no longer constant, right ?

the changing acceleration is not taught in high school physics, so a_av = Δv/Δt is enough for me.

 

[Chestermiller]

the acceleration "a" in these equations is instantaneous or average acceleration or both like Chestermiller said ?

Don't you believe me?

Chet

 

[stephenranger]

Don't you believe me?

Chet

Come on sir. I need multiple viewpoints to have a good comparison.
Your phrase:

The second equation is correct only if the acceleration is varying linearly with time.

gives me an idea that when acceleration is an equation of time it becomes instantaneous acceleration. Is that correct ?

 

[Chestermiller]

Come on sir. I need multiple viewpoints to have a good comparison.
Your phrase:

gives me an idea that when acceleration is an equation of time it becomes instantaneous acceleration. Is that correct ?

The following equations that you presented, s = v0t + 0.5at2 and vfi = vin + at and (vfi)2 - (vin)2 = 2as, are valid only if the acceleration is constant. Otherwise they will give the wrong answer. If the acceleration is constant, then the instantaneous acceleration is equal to the average acceleration.

Chet

 

[stephenranger]

The following equations that you presented, s = v0t + 0.5at2 and vfi = vin + at and (vfi)2 - (vin)2 = 2as, are valid only if the acceleration is constant. Otherwise they will give the wrong answer. If the acceleration is constant, then the instantaneous acceleration is equal to the average acceleration.

Chet

Yes. Could you tell me in what phenomenon will the acceleration be an equation of time, a = a_(t) ? and when I take its derivative da_(t)/dt, what does da_(t)/dt stand for ?
I ask that out of my curiosity.

 

[Chestermiller]

Yes. Could you tell me in what phenomenon will the acceleration be an equation of time, a = a_(t) ? and when I take its derivative da_(t)/dt, what does da_(t)/dt stand for ?
I ask that out of my curiosity.

The acceleration of a body is a function of time if the net force acting on the body is varying with time.

As far as the derivative of the acceleration with respect to time is concerned, I believe this quantity is called the "jerk."

http://en.wikipedia.org/wiki/Jerk_(physics)

Chet

 

[stephenranger]

The acceleration of a body is a function of time if the net force acting on the body is varying with time.

As far as the derivative of the acceleration with respect to time is concerned, I believe this quantity is called the "jerk."

http://en.wikipedia.org/wiki/Jerk_(physics)

Chet

Thanks very much.

 

[BruceW]

Chet has answered well, but I'm going to add my answer, if you're interested. In the general case, the acceleration is a function of time. It is only in special cases that the acceleration is constant. So, when the acceleration is not constant, as you say, we have: a_(t) a function of time. For example, you are in a car, and the car is accelerating forward, due to the driver pushing their foot down on the gas. You have to use your neck muscles to hold your head forward, due to the acceleration. But then, suppose the driver decides to put their foot down on the gas even more, so acceleration increases, and your head would be pushed backwards, unless you strained your neck muscles even more. So this intuitively explains why the rate of change of acceleration is called the jerk.

 

[stephenranger]

Chet has answered well, but I'm going to add my answer, if you're interested. In the general case, the acceleration is a function of time. It is only in special cases that the acceleration is constant. So, when the acceleration is not constant, as you say, we have: a_(t) a function of time. For example, you are in a car, and the car is accelerating forward, due to the driver pushing their foot down on the gas. You have to use your neck muscles to hold your head forward, due to the acceleration. But then, suppose the driver decides to put their foot down on the gas even more, so acceleration increases, and your head would be pushed backwards, unless you strained your neck muscles even more. So this intuitively explains why the rate of change of acceleration is called the jerk.

Thanks. Now I know the origin of its name.