Most human being use speed and also velocity interchangeably. Yet to physicists, the 2 have really specific, and also different, meanings. To complicate problem further, not all physics textbooks agree on the definition of speed.

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Today, i taught Alan Alda the difference between speed and velocity. Life is complete.

— Physics Girl (

But what is the difference? If girlfriend ask any type of person ~ above the street, they could say over there is no difference. In non-physics use, they would be correct. However, in physics we have very certain definitions for these terms. Surprisingly, not all textbooks agree top top the an interpretation of speed.

Let's begin with the simple term: velocity. I'm pretty sure all the textbooks agree on this definition.

Velocity and Average Velocity

I assumption: v I should start from the beginning. There space two other important terms: position and displacement. Mean that I have a moving object. It move from ar 1 to location 2 follow me the path displayed below.


The place of place 1 is the vector from the origin to that point. Exact same for location 2 and the place vector 2. Place is a vector indigenous the origin of her coordinate system to some specific point. If you change the place of the origin, your place vectors will change.

The displacement is the vector from location 1 to 2. This vector does NOT count on the ar of the origin. If you recognize the two place vectors, climate the displacement vector would be:


Finally, we are ready for the meaning of average velocity. As soon as the object goes from place 1 to 2, it will take some time. I will contact this time Δt. The average velocity would certainly then be:


That's the median velocity. Yet what about just velocity? Technically, this would certainly be dubbed instantaneous velocity. This is just the limit as the moment interval approaches zero. Of food that makes this a derivative through respect to time:


That's velocity. Pretty much everyone agrees on this definition.

Speed and also Average Speed

There room two common definitions of rate that are used in textbooks. Ns looked v a sample of books in mine office and all of them dropped into among two definitions.

Speed definition 1: The mean speed is the street traveled split by the moment it took to travel this distance. If I use the symbol s for speed (which isn't a very good choice), then I would certainly write:


You deserve to see the trouble here. How do you calculate distance? In the snapshot example above, this would be the length of the dotted line path. The average velocity just depends on the beginning and finishing point, not the path yet the speed depends on the path (in this definition). Likewise with this definition, the typical speed is a scalar quantity and not a vector quantity.

Oh, most of the textbooks supplied this an interpretation of average speed.

Speed definition 2: rate is the size of the velocity. That's it. As an equation, that would certainly be:


This would likewise make speed a scalar value.

An Example

Here is a standard example reflecting the difference in between average velocity and also the two interpretations of speed. Expect you have a circular race track that has actually a circumference of 1000 meters. A vehicle drives approximately the monitor such that it take away 50 secs for a lap. What is the average velocity and also the typical speed?


For the average velocity, I require the vector position of the start and end of the motion. However wait! These are in the same spot! That means that the displacement is the zero vector (which is different than just zero). The typical velocity is zero vector m/s. How can this be? Remember, the velocity is a vector. V an median velocity the zero (vector), that method the car is going just as much North as it is southern so that these all typical to zero (vector).

What about the median speed follow to an interpretation 1? In this case, the street traveled is 1000 meter so that the typical speed would certainly be (1000 m)/(50 s) = 20 m/s. This is what the speedometer would read.

According to definition number 2, the median speed is the magnitude of the average velocity. Since the average velocity is zero (vector) m/s, the size of this is likewise zero meters per second. If you desire the instantaneous speed according come the an interpretation 2, that would also be 20 m/s.

It's all around definitions

Suppose we desire to have actually a discussion about gardening. In this discussion, I store talking about a hand shovel (a tiny shovel that you deserve to use v one hand). However, you always call this a huge spoon for this reason that as soon as I to speak "hand shovel", you have no idea what ns am talking about. This situation seems silly, but we have this exact problem in physics.

Consider the word momentum. Whenever i am having a conversation with students about physics and also motion, this word has tendency to come up. But it is frequently used to mean lots of various things - choose pushing, energy, speed, and even momentum. In physics, we have a an extremely explicit definition for momentum.

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The inert (at velocities not close to the speed of light) is identified as the product of the mass and velocity of one object. This meaning physicists (and textbooks) agree on. The meaning of speed isn't constantly agreed on.