# Can a body have velocity and not move?

1. Aug 1, 2012

### lucasqueiroz

I have arrived at the contradictory conclusion that a body can have a positive or negative velocity and not be moving(variating it's space). It is contradictory because if it has a positive or negative velocity it must be moving (variating it's space) since velocity is a variation in space, as physicians represent it mathematically:V=ΔS/Δt. There must be something wrong with my reasoning but I am unable to find what it is.

Here is my reasoning:
In physics there is the formula F=m.a(Force is equal to mass mutiplied by acceleration).

If for example I press my hand against a wall, a physician would say that I am applying a force on the wall with my hand, so my hand's acceleration is different from 0, because if it were 0 the force would be 0.

Since my hand is accelerating it's speed is changing since acceleration is change in speed. From that it follows that there are moments where the velocity of my hand is either positive or negative, and therefore is moving(variating it's space). But my hand is not moving at all.

2. Aug 1, 2012

### AnthonyLiardo

In regards to your reasoning, the formula F = m$\cdot$a applies to the net force on a system. So the formula is really $\sum$F = m$\cdot$a

In regards to the first part, velocity is all relative. We're almost always thinking about being relative to the earth so sometimes it's confusing. If an object is in space and is "not moving," it may be moving very fast relative to a meteor or it can have zero velocity to that meteor if they're moving at the same speed.

The V = $\Delta$S / $\Delta$t is for relative change in position. I think time itself is also relative but I'm pretty sure (someone correct me if I'm wrong) the difference is negligible for "small" velocities like 0 - 1000 m/s or something like that.

3. Aug 1, 2012

### lucasqueiroz

Thanks for the explanation. Unfortunately I am a begineer in the study of physics and I do not understand symbols like this one Ʃ.

4. Aug 1, 2012

### krd

V = ΔS / Δt, is change in distance over time. If your hand isn't going anywhere, the change in distance is zero, which means, ΔS = 0, which means V = ΔS / Δt = 0, V = 0, which means there is no velocity.

If you're pressing against the wall, and your hand is going nowhere, it means the wall is recoiling all the force you're exerting against it. You can keep pushing, and feel the strain in your hand, but the wall will give as good as it gets, unless you're the incredible hulk, who can defeat the wall and press a hole through it. And then at that point your hand will have velocity.

There is no contradiction. If you press your hand against the wall, and it won't yield, you will feel the force coming back in your hand - usually mild pain and stress. The wall will feel stress too. The atoms in your hand and the wall will have been given momentum/velocity, but you won't see it.

5. Aug 1, 2012

### azizlwl

You apply a force and no acceleration on the wall.
There are many ways without accelerating the wall.
1. As you say you are not applying any force, F=0
2. You may apply a force and there's another force counteract it. As if you push you friend and your friend equally force back. Both of you remain stationary.
Both of you can also be stationary respective to each other if nobody pushing nobody.

This the symbol you are asking for, Ʃ. Means the total sum of forces acting on a body that results in any movement.

Ps.

A physicist is a scientist who does research in physics.

A physician is a health care provider who practices the profession of medicine, which is concerned with promoting, maintaining or restoring human health through the study, diagnosis, and treatment of disease, injury, and other physical and mental impairments.

Last edited: Aug 1, 2012
6. Aug 2, 2012

### sugeet

as put force against the wall, the wall put equal force on you, the starin energy in it,
to do work you need displacement first, first u need delta s before ub go to rate of change in delta s ; which is velocity