Defining Speed = Distance/Time, or ||Displacement||/Time?

[ahyaa]

Hello,

Given that distance is path-dependent and displacement measures only the net change, how do we define speed?

I have seen speed defined as 1) distance over time, and 2) the magnitude of velocity. I recognize that these are two different things because distance is path-dependent while velocity = displacement/time and displacement measures net change. Thus, which definition is the accepted definition for speed?

 

[Simon Bridge]

"Speed", in physics, is a technical term referring to the magnitude of the velocity vector.
In common language it has a number of different uses - most commonly referring to the distance traveled divided by the time taken.
In physics this second one would be properly called the average speed, but you need to watch for non-technical language.

Notice that if you complete a circle, then the displacement is zero, so the average velocity is zero so the speed was zero - even if you traveled in that circle very fast.

Note: "distance" would be the magnitude of the displacement vector - but there are other kinds of distances - in common language "distance" can mean the separation of two locations (also called "as the crow flies") or it can be the length of the path traveled for example.

 

[jtbell]

I have seen speed defined as 1) distance over time,

As Simon noted, this is the average speed during the specified time interval.

and 2) the magnitude of velocity.

This is the instantaneous speed at some point in time, provided that we use the instantaneous velocity at that point in time.

velocity = displacement/time and displacement measures net change

This gives you the average velocity during the specified time interval.

In general, the average speed during a specified time interval does not equal the magnitude of the average velocity during that time interval; whereas the instantaneous speed at any point in time equals the magnitude of the instantaneous velocity at that point in time.

In Simon's example, if you go around a complete circle at constant speed, then your average speed for the entire circle equals that constant speed, but your average velocity is zero because your net displacement is zero. Your instantaneous speed at every point on the circle equals that constant speed, and therefore the magnitude of the instantaneous velocity is the same at every point; but your direction changes continuously as you move around the circle, so your instantaneous velocity (which includes both magnitude and direction) is different at every point on the circle.

 

[ahyaa]

Got it, thank you all