Is this correct? Does we can say the body stops?

[SciencePF]

Suppose that an object is moving up an inclined plane, then stops and after moves down. Is correct to say that the objects stops, or we can only say that it inverts its motion without stopping?

 

[devoured_elysium]

There is a moment where it effectively stops. Otherwise, how could it invert its way of motion?

 

[CraigD]

It stops, but this raises the importance of sampling rates in experiments. If you are only sampling the speed of the object every 10 seconds, odds are you will not see it stopped. But if you sample the speed every femto second you have increased the odds incredably that you will see it stop. The balance comes in how much data can you retain and as sampling rates go up, cost goes up.

CraigD, AMInstP
www.cymek.com

 

[haiha]

Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.

 

[cesiumfrog]

haiha, you just failed the math exam

 

[cristo]

Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.

Huh?? How can the velocity of an object get from v to -v without passing through zero?

 

[haiha]

haiha, you just failed the math exam

With dt not zero, I can always find for you a dS >0 (or<0), that's my argument

 

[haiha]

Huh?? How can the velocity of an object get from v to -v without passing through zero?

You make me remember the problem of a bird flying between two trains approaching each other. Theoretically, it wil never stop.
This case i also marked as theoretical.

 

[Doc Al]

You make me remember the problem of a bird flying between two trains approaching each other. Theoretically, it wil never stop.
This case i also marked as theoretical.

If your theory predicts the bird will never stop, your theory needs to be revised.

 

[haiha]

Imagine the bird has no thickness (a mathematical point), and it always flies faster than the trains. It will never stop. But it ocsillates at increasing frequency.

 

[Doc Al]

The bird "stops" when it's crushed between the colliding trains. That's what enables you to calculate the distance it covered.

 

[Danger]

I know that the answer seems obvious; of course it stops. In reality, though, isn't it more likely that the ball or whatever would describe a very small circular path at the apex rather than simply reverse and come straight down? I realize that it could be restricted with rails or a groove or something, but that wasn't specified in the OP.

 

[nealh149]

haiha, dS/dt is not a fraction.

 

[cepheid]

I know that the answer seems obvious; of course it stops. In reality, though, isn't it more likely that the ball or whatever would describe a very small circular path at the apex rather than simply reverse and come straight down? I realize that it could be restricted with rails or a groove or something, but that wasn't specified in the OP.

Oh yeah? Well I just redefined this as a 1D problem...it's a circle rolling up an inclined "line".

 

[cepheid]

haiha, you just failed the math exam

Ouch. The truth hurts sometimes...yes a review of basic calculus is definitely in order.

 

[haiha]

Ouch. The truth hurts sometimes...yes a review of basic calculus is definitely in order.

Never mind, it's a good thing. I've been doing it.

 

[KingNothing]

haiha, dS/dt is not a fraction.

Yes, it is.

 

[ice109]

Yes, it is.

no it isn't

 

[Danger]

Alright, you two... behind the bike racks after school...

 

[prasannapakkiam]

What does a fraction have anything to do with the question?

In order for the ball to change direction, the line in the v vs t graph has to go throught eh x-axis. An interesting topic would be to argue how long this 'stop' is.

 

[cristo]

What does a fraction have anything to do with the question?

This discussion regarding fractions came about due to this post:

Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.

ds/dt is a derivative, but is treated above as if it is a fraction. This is incorrect.

 

[tim_lou]

com'on... Rolle's theorem says, the bird does stop. Unless the velocity function is not continuous, which in normal real life, doesn't really happen.

 

[Manu Vincent]

Yes, we can say that the body stops

If the body is in motion, then we can sat that the velocity of the body is positive. And at rest or when the body stops the velocity is zero, even though the body stops only for a moment at a particular instance the velocity is zero. After the rest the velocity increases with a negative sign but the motion does not invert, only the direction of the motion.And the it accelarates in the downward motion.

 

[haiha]

I still keep the idea that when we say something stops, there must be a piece of time in which the body's position is unchanged, in this case, we can not find that piece of time. The velocity can be zero at certain point of time, but that does not mean it stops. It is something like a car which has problem in the carburetor that it can not goes smoothly, but it doesn't stop.
Another example is the cycloid movement. A point on the rim of a ring is on the move all the time when the ring is rolling on a surface. When it contacts with the surface, its velocity is zero for a moment. But we can not say it stops even then.

 

[moose]

Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.

By your reasoning, it will also never have a velocity of 1, or 2, or 1.1, or 54, or whatever you choose!

 

[haiha]

By your reasoning, it will also never have a velocity of 1, or 2, or 1.1, or 54, or whatever you choose!

I think we may mix the words stops and zero velocity.

 

[Doc Al]

I think we may mix the words stops and zero velocity.

That might explain the problems here. In the context of the initial post, "stop" means have a velocity = 0. Just for an instant, of course--not for some finite interval.