The discussion revolves around understanding the concepts of average and instantaneous acceleration, particularly in the context of various kinematic equations. Participants explore the definitions and applications of these terms in physics, questioning the validity of certain formulas and their assumptions.
The conversation includes multiple viewpoints on the nature of acceleration in different scenarios. Some participants provide clarifications and corrections, while others seek further understanding of the implications of varying acceleration and its mathematical representation.
There is an emphasis on the distinction between constant and varying acceleration, with references to high school physics limitations. Participants express curiosity about the implications of acceleration as a function of time and its derivative, known as "jerk."
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.stephenranger said:Homework Statement
This is not a homework, just my understanding problem.
Homework Equations
We know that average acceleration can be calculated by: aav=Δs/Δt
Is this formula also correct: aav=0.5(afi+ain) ??
Both. These equations assume that the acceleration is constant, so it is both the instantaneous acceleration and the average acceleration.One more question is: in the formulas: s = v0t + 0.5at2 and vfi = vin + at and (vfi)2 - (vin)2 = 2as
a in these equations is instantaneous acceleration or average acceleration ?
A correct statement is: aav=Δv/Δt .stephenranger said:...
We know that average acceleration can be calculated by: aav=Δs/Δt
Yes. I have a typo, sorry.SammyS said:A correct statement is: aav=Δv/Δt .
Perhaps you had a typo.
Also true is vav=Δs/Δt .
stephenranger said:s = v0t + 0.5at2 and vfi = vin + at and (vfi)2 - (vin)2 = 2as
Yes sir. if the acceleration is varying linearly with time, that means that it's no longer constant, right ?Chestermiller said:The second equation is correct only if the acceleration is varying linearly with time.
Don't you believe me?stephenranger said:the acceleration "a" in these equations is instantaneous or average acceleration or both like Chestermiller said ?
Come on sir. I need multiple viewpoints to have a good comparison.Chestermiller said:Don't you believe me?
Chet
gives me an idea that when acceleration is an equation of time it becomes instantaneous acceleration. Is that correct ?Chestermiller said:The second equation is correct only if the acceleration is varying linearly with time.
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.stephenranger said: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 ?
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 ?Chestermiller said: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
The acceleration of a body is a function of time if the net force acting on the body is varying with time.stephenranger said: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 said: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
BruceW said: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.