Is it possible to have zero velocity and zero acceleration?

[persia77]

is it possible to have zero velocity and zero acceleration for a moving object
for example with trajectory x= (t-2)^3
at t=2
a=v=0

 

[A.T.]

zero velocity ... for a moving object

How do you define "moving"?

 

[persia77]

How do you define "moving"?

move=change of location

 

[PeroK]

I guess you mean instantaneously 0. For example, an object could stop for a second and then start again. It would have 0 velocity and acceleration for 1 second as part of its motion.

If you imagine an object at rest subject to a force proportional to t. F = t, say. Then at t = 0 it would have 0 velocity and acceleration, yet it would start moving at t = 0.

 

[Khashishi]

It's clear that you understand velocity and acceleration from your given example. The language of math is clear on this one. I wouldn't worry about "moving" or not.

 

[russ_watters]

I'm sitting on my couch right now, with zero velocity and zero acceleration.

 

[nasu]

But are you "a moving object"? :)

 

[phinds]

But are you "a moving object"? :)

There are an infinite number of Frames of Reference in which he is a moving object. Only in his own Frame of Reference is he not moving (and that's not counting the arm motions required to drink his beer and click the TV remote).

 

[russ_watters]

There are an infinite number of Frames of Reference in which he is a moving object. Only in his own Frame of Reference is he not moving.

It's not my frame, it's my couch's -- I'm just in (on) it temporarily.

 

[phinds]

It's not my frame, it's my couch's -- I'm just in (on) it temporarily.

Fair enough

 

[persia77]

It's not my frame, it's my couch's -- I'm just in (on) it temporarily.

you are not moving object in your coachs frame
you should say a frame that you are a moving object in it and have instantaneous zero velocity and acceleration

 

[phinds]

you are not moving object in your coachs frame
you should say a frame that you are a moving object in it and have instantaneous zero velocity and acceleration

Do you understand that "moving" and "having velocity" mean exactly the same thing? You are asking if something can be moving and not moving at the same time. Well ... no. At the time when something has zero velocity it is not moving. If you want something that is moving irregularly (fast sometime, slow sometimes, not at all sometimes) then you can certainly have something that is moving most of the time and not moving some of the time. BUT ... if you are transitioning from moving to not moving, that is called "acceleration" so you can't have something that is moving some of the time and then not moving and having zero acceleration as it come to a stop. Once it has been AT at a stop for a small amount of time, then it will have zero acceleration.

I'm not sure you understand what velocity and acceleration imply and/or I'm not sure what you are asking. It sounds very confused. In your example, yes v=0 at t=0 but the acceleration at that point is not zero because it is transitioning from v=0 to v not = 0 and that is called acceleration.

Do you understand how, mathematically, to get the acceleration of your example? If x = (t-2)^3 then what operation do you perform to get the acceleration? If you perform that operation, you will see clearly that the acceleration is not zero.

 

[russ_watters]

you are not moving object in your coachs frame
you should say a frame that you are a moving object in it and have instantaneous zero velocity and acceleration

Why? Doesn't that make the original question sort of circular and contradictory? Basically when you combine the two, you get: "Is it possible to be stationary in a frame where you are moving?" Well, no -- if you are stationary, you aren't moving and if you are moving, you aren't stationary.

 

[PeroK]

Do you understand how, mathematically, to get the acceleration of your example? If x = (t-2)^3 then what operation do you perform to get the acceleration? If you perform that operation, you will see clearly that the acceleration is not zero.

There is something of a paradox here, since at t = 2, we have:

x = 0, v = 0 and a = 0

Yet, for any t > 2, the particle has a non-zero displacement. It's instantaneously at rest and, also, instantaneously has 0 acceleration.

It's just the same puzzle as how the function $y=x^3$ manages to get back up off the x-axis after x=0.

 

[phinds]

It's just the same puzzle as how the function $y=x^3$ manages to get back up off the x-axis after x=0.

It's constrained motion. It's moving that way by definition, whatever the force(s) required to make it do so.

I do thing, however, that you have pointed out a flaw in my own thinking. In this example, which is as good as any, i see (ignoring the math) that the object is going from zero motion to non-zero motion so I see it as accelerating, BUT ... the math says a=0.

 

[persia77]

It's constrained motion. It's moving that way by definition, whatever the force(s) required to make it do so.

I do thing, however, that you have pointed out a flaw in my own thinking. In this example, which is as good as any, i see (ignoring the math) that the object is going from zero motion to non-zero motion so I see it as accelerating, BUT ... the math says a=0.

you don't understand what velocity and acceleration is
acceleration is derivation of velocity
do you understand meaning of derivation ?

 

[persia77]

Why? Doesn't that make the original question sort of circular and contradictory? Basically when you combine the two, you get: "Is it possible to be stationary in a frame where you are moving?" Well, no -- if you are stationary, you aren't moving and if you are moving, you aren't stationary.

my first example shows your statement is wrong
a moving object
with trajectory x= (t-2)^3
at t=2
instantaneous a=v=0

 

[PeroK]

my first example shows your statement is wrong
a moving object
with trajectory x= (t-2)^3
at t=2
a=v=0

But, it's not "moving" at t = 2. It's moving at all other times, but it's instantaneously at rest at t = 2.

 

[persia77]

But, it's not "moving" at t = 2. It's moving at all other times, but it's instantaneously at rest at t = 2.

a moving object can have instantaneous zero velocity at some moment

 

[PeroK]

a moving object can have instantaneous zero velocity at some moment

It can have 0 velocity for as long as you like. I already pointed that out to you. It can move, stop for a second, then move again. It's still a "moving object", it's just not moving all the time.

 

[persia77]

It can have 0 velocity for as long as you like. I already pointed that out to you. It can move, stop for a second, then move again. It's still a "moving object", it's just not moving all the time.

if you drop a ball in the air (to up) it has instantaneous zero velocity at top of its trajectory but it is a moving object all the time

 

[PeroK]

if you drop a ball in the air (to up) it has instantaneous zero velocity at top of its trajectory but it is a moving object all the time

The mathematics says otherwise.

 

[jbriggs444]

This seems to amount to nothing more than a word game. We need to pin down a definition of "moving".

Definition:

An object whose position is given by x(t) is "moving" at time t if and only if for all epsilon > 0 there is a strictly positive delta such that |delta| < epsilon and x(t+delta) != x(t).

Definition:

An object is "moving" over an open interval if it is moving at all times that fall within that interval.

Claim:

An object can be "moving" over the interval from t=0 through t=4 and have zero velocity and zero acceleration at t=2.

 

[persia77]

The mathematics says otherwise.

no
The mathematics says exactly same

 

[PeroK]

no
The mathematics says exactly same

At the top of its trajectory, in which direction is it moving?

 

[persia77]

This seems to amount to nothing more than a word game. We need to pin down a definition of "moving".

Definition:

An object whose position is given by x(t) is "moving" at time t if and only if for all epsilon > 0 there is a strictly positive delta such that |delta| < epsilon and x(t+delta) != x(t).

Definition:

An object is "moving" over an open interval if it is moving at all times that fall within that interval.

Claim:

An object can be "moving" over the interval from t=0 through t=4 and have zero velocity and zero acceleration at t=2.

can you show a real physical example

 

[persia77]

At the top of its trajectory, in which direction is it moving?

its not important
it is moving object with instantaneous zero velocity

 

[jbriggs444]

can you show a real physical example

What has a real physical example to do with this purely mathematical and linguistic discussion?

However...

One can contrive an example of a charged puck moving north on a hockey rink that is subjected to a southward electric field that is decreasing smoothly over time. Exactly as the puck achieves zero velocity, the electric field reaches zero and begins increasing in the northward direction.

The puck had zero velocity when the electric field was zero. But it was "moving" throughout the exercise. There was no finite time interval of non-zero extent during which its position was constant.

 

[A.T.]

its not important

If your definition of "moving" doesn't even require a direction, what physical relevance does your definition of "moving" have, and why should we even care about that type of "moving"?

 

[persia77]

One can contrive an example of a charged puck moving north on a hockey rink that is subjected to a southward electric field that is decreasing smoothly over time. Exactly as the puck achieves zero velocity, the electric field reaches zero and begins increasing in the northward direction.

The puck had zero velocity when the electric field was zero. But it was "moving" throughout the exercise. There was no finite time interval of non-zero extent during which its position was constant.

does it have instantaneous zero velocity and instantaneous zero acceleration simultaneously?

 

[jbriggs444]

does it have instantaneous zero velocity and instantaneous zero acceleration simultaneously?

Yes, I stipulated that:

Exactly as the puck achieves zero velocity, the electric field reaches zero and begins increasing in the northward direction.

 

[persia77]

If your definition of "moving" doesn't even require a direction, what physical relevance does your definition of "moving" have, and why should we even care about that type of "moving"?

direction is zero at instantaneous zero velocity :)

 

[jbriggs444]

direction is zero at instantaneous zero velocity :)

The normal definition of the "direction" of a vector quantity would involve the vector being divided by its magnitude. The result has a magnitude of 1 and may be referred to as a "unit vector" or "direction vector". In the case of a zero vector, this involves division by zero. The direction of the zero vector is not defined.

 

[A.T.]

direction is zero

Sounds like your definition of "direction" is just as useful as your definition of "moving".

 

[persia77]

Sounds like your definition of "direction" is just as useful as your definition of "moving".

useful for u