They are completely different concepts, in short:
Force = mass * acceleration
Acceleration = Velocity / time
Velocity = distance-traveled / time
It's actually incorrect more so than clear.
Distance traveled divided by time is not velocity. It's speed, a scalar value.
Velocity has to do with the rate of change and is represented by a vector providing direction, and it's magnitude representing speed. So while speed is the simple speed an object travels at, velocity also specifies direction.
A force is represented similarly to velocity and has/affects (depending on the approach, generally correct if considered affecting) mass, it's effect results in the affected body's velocity. A force is basically something affecting another entity into change. It can be summarized in push or pull efforts.
Acceleration is the rate of change of speed.
This is for Newtonian physics, or vectorial physics, the most common kind in CG related models.
Thank's César ! Now it's clear :)
Reading that after sending it (when else would one proof read?) I realize it might come across as a bit aggressive with the opening comment.
My apologies to César if that's the case, it sure wasn't intended to be or to discourage someone else away from contributing to the already rare physics discussions.
Oliver, Wikipedia has excellent resources about these subjects, just look up Newtonian physics and wiki hop around to the specific words you wanted the meaning of.
Yes it’s important because there are many equations which rely on velocity as a variable, not speed.
If you’re computing a speed, you need to accumulate the distance travelled over time. If you’re computing a velocity, you’re working with deltas.
In more explicit terms, if you’re computing motion vectors, you’re comparing the current frame to the previous frame. If you’re computing speed, you’re comparing the current frame to the first frame. How you code for those scenarios is vastly different.
Matt

If you have a problem with the definitions, talk to mathematicians and physicists.
I only put out the information for clarity as confusing speed with velocity is very common and there are times when it does indeed matter.
I gave the same definition and example as was used when I learned it in physics class all those years ago. I don’t recall anybody having a problem with it then.
Matt
From: softimag...@listproc.autodesk.com [mailto:softimag...@listproc.autodesk.com] On Behalf Of Steven Caron
Sent: Wednesday, February 13, 2013 1:46 PM
To: soft...@listproc.autodesk.com
Subject: Re: Difference between a force and a velocity ?
i have no problem with the definitions and i just thought you might actually be causing more confusion with your example.

I’m not perturbed, I just don’t think your assessment is accurate based on past experience of the subject being taught.
I think its other people who are blowing this out of proportion. After sending my initial email on the subject, I encountered this one from Olivier which precedes mine:
>Thank's César ! Now it's clear :)
>
>Le 13/02/2013 11:13, César Sáez a écrit :
>
> They are completely different concepts, in short:
>
> Force = mass * acceleration
>
> Acceleration = Velocity / time
>
> Velocity = distance-traveled / time
>
Seeing how I didn’t do much differently than Caesar as far as explanation other than to give an example, I don’t think I’ve done anything to split hairs or mislead people. I gave a very introductory explanation as is normally given on the 1st or 2nd day of a physics course. If you want to dive deeper and differentiate between instantaneous velocities and whatever everybody else is throwing about, then you are the ones splitting the hairs, not me.
There’s nothing wrong with the running track example. You are overthinking the problem. It’s an introductory level illustration to clarify the difference between speed (scalar) and velocity (vector), and is used in physics text books believe it or not. If you do a google search on “physics definition of velocity”, the top three results all explain velocity as the change in position divided by the change in time. (e.g. v = x1 – x0 / t1 – t0). If the start position and end position are the same, then the velocity is indeed zero over any time interval because it has no magnitude, and proven mathematically. If you have a problem with that, take it up with the physicists and mathematicians.
From: softimag...@listproc.autodesk.com [mailto:softimag...@listproc.autodesk.com] On Behalf Of Andy Jones
Sent: Wednesday, February 13, 2013 6:08 PM
To: soft...@listproc.autodesk.com
Subject: Re: Difference between a force and a velocity ?
The example of running around on a track is wrong unless you're on a stationary planet. Way to confuse Olivier, guys :(
Apologies, there are a couple of number typos in the first one.
Here is the corrected version:
Velocity is the speed and direction at which an object moves.Force is something with a strength and a direction that causes acceleration on the object and has an effect on its velocity.
Think about it like this:You have some object, that is flying through space with a VELOCITY.
Maybe it is flying upwards, so the DIRECTION it is flying in would be [0, 1, 0].And let's say that it is flying with a SPEED of 6 units per second.
Those are the two components our velocity is made of: In what direction is it flying and how fast is it flying there?
In ICE these two values are one vector [0, 6, 0] which you get by multiplying the SPEED (6) with the DIRECTION ([0, 1, 0]).When you multiply a vector(a row of numbers) with a scalar(a single number) you simply multiply each element of the vector with the scalar.[6*0, 6*1, 6*0] = [0, 6, 0] = the VELOCITY of the object
Now there is also the FORCE and this could be for example gravity or a wind blowing, just anything that will move the object.What properties does a force have?It pushes things in a certain DIRECTION.It pushes things with a certain STRENGTH.
Let's say our force pushes to the left, so in Softimage it's DIRECTION would be [1, 0, 0].And let's say that the STRENGTH of the forces push is 8.
Once again these two properties of the force are represented in one vector [8, 0, 0] which you get by multiplying the STRENGTH(8) with the DIRECTION ([1, 0, 0]).[8*1, 8*0, 8*0] = [8, 0, 0] = the FORCE.
So now that we have a good idea of what a force and a velocity are let's see what happens when the force acts upon our little object.
The object is moving through space with the VELOCITY [0, 6, 0] and suddenly there is the FORCE [8, 0, 0] acting on it. Maybe an interstellar wind started blowing...The FORCE is acting on the object and wants to push it in another direction/speed, which would give it a new VELOCITY since velocity = speed*direction.But the object also has MASS, that is a measure of how resistant to changing velocity an object is. Let's say it has the MASS 4.
Now the force is still going to change the velocity of the object, but the effect will be reduced by the mass.The formula for how it is going to be reduced by the mass, comes from the famous formula F=m*a ( force = mass * acceleration )If we divide both sides of that equation by mass we get:F/m = a ( force / mass = acceleration)This tells us that we must divide our FORCE (F) by the MASS (m) to get the acceleration.Force: [8, 0, 0]Mass: 4[8, 0, 0] / 4 = [8/4, 0/4, 0/4 = [2, 0, 0] = acceleration
Now all you have to do once you have computed your acceleration is to add it your velocity, to see what new velocity the force pushed it in.So: PreForceVelocity + acceleration = PostForceVelocityVelocity = [0, 6, 0]Acceleration = [2, 0, 0][0, 6, 0] + [2, 0, 0] = [0+2, 6+0, 0+0] = [2, 6, 0] = PostForceVelocity
After our Object travelling with a mass of 4 and a velocity of [0, 6, 0] interacted with a force of [8, 0, 0] its new velocity is [2, 6, 0]
A bit elaborate, but I hope it helps you gain some intuition.
On Wed, Feb 13, 2013 at 12:24 PM, Leonard Koch <leonard...@gmail.com> wrote:
Velocity is the speed and direction at which an object moves.Force is something with a strength and a direction that causes acceleration on the object and has an effect on its velocity.
Think about it like this:You have some object, that is flying through space with a VELOCITY.
Maybe it is flying upwards, so the DIRECTION it is flying in would be [0, 1, 0].And let's say that it is flying with a SPEED of 6 units per second.
Those are the two components our velocity is made of: In what direction is it flying and how fast is it flying there?
In ICE these two values are one vector [0, 6, 0] which you get by multiplying the SPEED (5) with the DIRECTION ([0, 1, 0]).When you multiply a vector(a row of numbers) with a scalar(a single number) you simply multiply each element of the vector with the scalar.[6*0, 6*1, 6*0] = [0, 6, 0] = the VELOCITY of the object
Now there is also the FORCE and this could be for example gravity or a wind blowing, just anything that will move the object.What properties does a force have?It pushes things in a certain DIRECTION.It pushes things with a certain STRENGTH.
Let's say our force pushes to the left, so in Softimage it's DIRECTION would be [1, 0, 0].And let's say that the STRENGTH of the forces push is 8.
Once again these two properties of the force are represented in one vector [2, 0, 0] which you get by multiplying the STRENGTH(8) with the DIRECTION ([1, 0, 0]).[8*1, 8*0, 8*0] = [8, 0, 0] = the FORCE.
So now that we have a good idea of what a force and a velocity are let's see what happens when the force acts upon our little object.
The object is moving through space with the VELOCITY [0, 6, 0] and suddenly there is the FORCE [8, 0, 0] acting on it. Maybe an interstellar wind started blowing...The FORCE is acting on the object and wants to push it in another direction/speed, which would give it a new VELOCITY since velocity = speed*direction.But the object also has MASS, that is a measure of how resistant to changing velocity an object is. Let's say it has the MASS 4.
Now the force is still going to change the velocity of the object, but the effect will be reduced by the mass.The formula for how it is going to be reduced by the mass, comes from the famous formula F=m*a ( force = mass * acceleration )If we divide both sides of that equation by mass we get:F/m = a ( force / mass = acceleration)This tells us that we must divide our FORCE (F) by the MASS (m) to get the acceleration.Force: [8, 0, 0]Mass: 4[8, 0, 0] / 4 = [8/4, 0/4, 0/4 = [2, 0, 0] = acceleration
Now all you have to do once you have computed your acceleration is to add it your velocity, to see what new velocity the force pushed it in.So: PreForceVelocity + acceleration = PostForceVelocityVelocity = [0, 6, 0]Acceleration = [2, 0, 0][0, 6, 0] + [2, 0, 0] = [0+2, 6+0, 0+0] = [2, 6, 0] = PostForceVelocity
After our Object travelling with a mass of 4 and a velocity of [0, 6, 0] interacted with a force of [8, 0, 0] its new velocity is [2, 6, 0]
A bit elaborate, but I hope it helps you gain some intuition.
On Wed, Feb 13, 2013 at 12:16 PM, Raffaele Fragapane <raffsx...@googlemail.com> wrote:
Reading that after sending it (when else would one proof read?) I realize it might come across as a bit aggressive with the opening comment.
My apologies to César if that's the case, it sure wasn't intended to be or to discourage someone else away from contributing to the already rare physics discussions.Oliver, Wikipedia has excellent resources about these subjects, just look up Newtonian physics and wiki hop around to the specific words you wanted the meaning of.
On Feb 13, 2013 10:08 PM, "Raffaele Fragapane" <raffsx...@googlemail.com> wrote:
It's actually incorrect more so than clear.
Distance traveled divided by time is not velocity. It's speed, a scalar value.
Velocity has to do with the rate of change and is represented by a vector providing direction, and it's magnitude representing speed. So while speed is the simple speed an object travels at, velocity also specifies direction.
A force is represented similarly to velocity and has/affects (depending on the approach, generally correct if considered affecting) mass, it's effect results in the affected body's velocity. A force is basically something affecting another entity into change. It can be summarized in push or pull efforts.
Acceleration is the rate of change of speed.
This is for Newtonian physics, or vectorial physics, the most common kind in CG related models.

is the magnitude of the velocity.Like I said multiple times already. Take it up with the physicists and mathematicians. The example given is from a physics text book. You got a problem, take it up with the author.
Sheesh!
From: softimag...@listproc.autodesk.com [mailto:softimag...@listproc.autodesk.com] On Behalf Of Alok Gandhi
Sent: Thursday, February 14, 2013 5:15 AM
To: soft...@listproc.autodesk.com

----- No virus found in this message. Checked by AVG - www.avg.com Version: 2012.0.2238 / Virus Database: 2639/5601 - Release Date: 02/13/13
Thanks for the validation, Brad.
Each instructor has their own methods because this was indeed the first example presented to me when I took physics years ago to make the distinction between speed and velocity. The professor said straight up it would be the very first question on the exam (it was) and anybody who got the question wrong would fail the exam. Nobody failed, to my knowledge. It wasn’t treated as a trick question, it was fundamental material.
He often reused examples across different topics so we could focus on the relevant new information and cut down the noise/relearning. For example, the running track was reused (with slight modifications) as an introduction to ‘work’ illustrating no work is performed if there is no displacement. Since he already proved the theory with velocity, he didn’t have to waste time re-explaining it for work. While tough at first due to the abstract nature, I found his approach very refreshing as it allowed me to tackle tougher problems because I was exposed to the edge cases upfront and conditioned to not think of them as edge cases. Edge cases are a product of our tools (math) to explain observed behavior. The universe doesn’t have a concept of edge case.
I think my professor chose this approach because he once mentioned students had problems progressing from newton’s laws to quantum mechanics because as they entered more advanced levels, they tended to forget previously learned material still applied (or they didn’t see the connection). He conditioned students to think more about the problem rather than merely choose a formula and plug in numbers. Often his toughest problems required the least amount of math to solve. Some of his lectures could be really dry, as he was a dry guy himself, but he was probably the best physics professor I had of many.
Matt
From: softimag...@listproc.autodesk.com [mailto:softimag...@listproc.autodesk.com] On Behalf Of Bradley Gabe
Sent: Thursday, February 14, 2013 1:21 PM
To: soft...@listproc.autodesk.com
Subject: Re: Difference between a force and a velocity ?
In the past 2 years, I attended college courses in Physics 101 and 201 at UT Dallas, as well as a Princeton Review course for the MCAT's which include heavy study in basic physics, especially about the definitions of fundamental units and concepts.
Awesome Gustavo, yes you broke it out perfectly!
The big plus with this multi-node approach is that you can do stuff I haven't implemented, like rotate the texture, or more easily mix several matcaps together, add bump etc (though I guess you could do that with the single shader, too.)
The shader I made is the bare bones, I strongly urge anyone interested to dive in. I'd love it if someone better at this kind of thing blew my little shader out of the water with something more robust.
If we can get a really strong solution it will be a major boon, just look at the mileage Zbrush users get out of matcap shading - it's a very robust way to shade, in particular for modeling/sculpting and for stills.