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

1. May 31, 2007

### 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?

2. May 31, 2007

### devoured_elysium

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

3. May 31, 2007

### 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

4. May 31, 2007

### 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.

5. May 31, 2007

### cesiumfrog

haiha, you just failed the math exam

6. May 31, 2007

### cristo

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

7. May 31, 2007

### haiha

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

8. May 31, 2007

### haiha

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.

9. May 31, 2007

### Staff: Mentor

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

10. May 31, 2007

### 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.

11. May 31, 2007

### Staff: Mentor

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

12. May 31, 2007

### 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.

13. May 31, 2007

### nealh149

haiha, dS/dt is not a fraction.

14. May 31, 2007

### cepheid

Staff Emeritus
Oh yeah??? Well I just redefined this as a 1D problem...it's a circle rolling up an inclined "line". :rofl: :tongue2:

15. May 31, 2007

### cepheid

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

16. Jun 1, 2007

### haiha

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

17. Jun 1, 2007

### KingNothing

Yes, it is.

18. Jun 1, 2007

### ice109

:uhh: no it isn't

19. Jun 2, 2007

### Danger

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

20. Jun 2, 2007

### 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.