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?

[ajb]

Distance divided by time gives you the average speed, which at constant velocity will be the same as the magnitude of the velocity.

 

In full generality you need to consider the instantaneous speed at a given time, which is the magnitude of the velocity.

[ahyaa]

Well said, thank you

[JonG]

Apologies in advance for being a little off-topic, but I read recently in a book by G.J.Whitrow that the ancient Greek mathematicians didn't get round to a clear definition of speed. The reason given was they regarded a fraction as the ratio of the size of one thing to another thing of the same type, so that they could divide a length by a length, for example, but not a length by a time. It this is true, it seems odd that people who were so adept at geometry were so awkward when it came to algebraic matters.