# Why do we care about the difference between speed and velocity?

I teach 7th grade students about the difference between speed and velocity. One of them ask me why do physicists create the concept of velocity. I cannot answer. I don't know precisely why do we care about the difference between speed and velocity.

• What research have you done to find an answer?! You have the entire resources of the internet at your fingertips. Are you telling us that you haven't been able to find an answer anywhere? You have a rep of 1200. You ought to know what is expected by now. – sammy gerbil Oct 11 '16 at 20:47
• Hi! I understand your concern. Not that I don't know the answer to this question. I got a master degree in Physics. However, I am a new teacher and this is the first time I try to explain this to 7th graders, someone that never study physics as a standalone subject before. My aim is to listen to new methods of communicating this to young students without too much math because, unsurprisingly, they hate math. – TBBT Oct 12 '16 at 5:35

We care so that we can conveniently calculate motion in 2- or 3-D.

Most motion important to us happens in 2- or 3-D (cars moving over land, airplanes flying through the sky, etc). Vectors make it convenient to handle quantities in more than 1 dimension, so we use vector quantities for position, velocity, and acceleration when describing 2- or 3-D motion.

We care so that we can find out the motion of things being pushed/pulled in different directions.

Not all motion happens along a straight line. Forces do not always push along a single direction. For example, shooting a basketball entails that you push the basketball upward and forward, while gravity pulls it downward. The basketball quite clearly does not move in a straight line; it moves in a curve, constantly changing direction.

In cases like these, we use vectors to describe motion. Vectors make it convenient to handle quantities going in different directions, because they were designed precisely to handle directions!

This is why we have the concept of a vector velocity (as well as position and acceleration): to handle motion where different directions are involved.

• Additional note: this answer may be a tad simplistic, but I believe it's a great way to teach 7th graders. – Ian Emnace Oct 11 '16 at 2:06
• They would not know what dimension is. – TBBT Oct 11 '16 at 3:31
• Oh, is that so? Can you try with concepts of axes or anything similar? I thought 7th grade math subjects already use y- and x-axes? – Ian Emnace Oct 11 '16 at 4:14
• Not here in Cambodia, they don't. – TBBT Oct 11 '16 at 5:42
• @TBBT Another example that would've helped me in 7th grade: If a car crashes into another car, what happens next depends not only on how fast the first car was going, but also on what direction it was going. – MissMonicaE Oct 12 '16 at 13:08

I give you a different type of answer. In Italian, and in many other languages I suppose, there are not different words for speed and velocity and so there is not any ambiguity among these concepts. Velocity it's a vector, but you can refer to it's module because there is not any ambiguity, as you do for any vector quantity. (For istance, I'm sure you would not have made the same question for the momentum) I think in English you stress the difference between the two only because in your language there were two different words (one from Latin and one from Germanic origins) already before the birth of physics. In my opinion is only a cultural difference.

• Right! All vectors have a length, but the length of the velocity vector has a special name in English: speed. – EL_DON Oct 12 '16 at 13:05
• Average speed would be path length divided by total time take while the magnitude of the velocity vector will be the magnitude of the displacement vector divided by the same time. So they both don't have to be the same right? When path length is longer than displacement I mean. – Aditya Mar 16 at 6:59
• I think this is well covered here - physics.stackexchange.com/a/54353/47252 – Aditya Mar 16 at 7:32

A mathematical description of the differences between speed and velocity is simple enough, and definitely essential; this has been elaborated upon by some of the answers here already. As far as the question "why should we care" goes, or how to get 7th graders interested well...more reasons than I can probably think of. Try something like sports. A quarterback can throw a football fast (speed), but its not going to do any good unless he throws it to the right place (trajectory and or velocity)... Or driving. You can drive the speed limit all you desire, but you will still get a ticket (or worse) if you are driving down the wrong side of the road (trajectory, velocity). Physicist care about these and their differences for similar reasons, but perhaps applied to a wide variety of different scenarios. Try getting them to think of some scenarios of their own by their own imaginations that they can apply them to, and explain the differences perhaps?

• Good idea. I will try to incorporate this. – TBBT Oct 12 '16 at 5:32

Speed is a scalar, velocity is a vector. We care because it gives us more information.

In three dimensional space velocity is expressed with three numbers, the speed in each of the three dimensions.

• How can I communicate this to 7th graders? – TBBT Oct 11 '16 at 3:29
• Perhaps it could be explained in two dimensions with diagrams. The concept might be broached by describing position as a vector (using different words) and then expanding to velocity. – mattfitzgerald Oct 11 '16 at 4:47
• Perhaps an example that shows the significance could be running towards a road (say) at an angle and talking about speed towards the road, speed in the direction of the road and then velocity. – mattfitzgerald Oct 11 '16 at 4:53
• @TBBT Drawing om mattfitzgeralds comments, try this: have them calculate the position of an object moving at ~1.41 m/s at a 45 degree angle on some 2d Grid. This is going to require trigonometry. Then, have them calculate the position of an object moving at a velocity of [+1 m/s X axis], [+1 m/s Y axis]. It's the exact same motion, but vectors make it so much easier. – UIDAlexD Oct 12 '16 at 13:05

Velocity includes information about direction as well as speed (magnitude of velocity). Suppose you are driving at a speed of 50 mph on a road with a washed out bridge, would you not also appreciate knowing your velocity? If you only know your speed you would not know whether you were driving toward or away from the washed out bridge. To make the distinction clear to your students, you might point out that a steering wheel is a device for altering velocity while maintaining constant speed.

• Would you expand of this please? I am not sure if I understand your answer. – TBBT Oct 11 '16 at 3:30
• See my edited answer. – Lewis Miller Oct 12 '16 at 12:59

If two trains approach each other from opposite directions, on the same train track, they need to calculate their "relative velocities" in order to determine when to stop before they collide. Of course, they would need to know their accelerations too, but if you're explaining to children, this might help. In this case, you can't only consider the "speed" of one train, you need to take into account their directions and each others' velocities (or magnitude of speed, and collude that with direction) to know when they would cross or meet at a certain point. This specific scenario, or others similar in nature, cannot be handled with only speed but require velocities, or rather, relative velocities.

## protected by Qmechanic♦Oct 11 '16 at 6:49

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