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This Is the Definition of Velocity That You Should Use In Physics
If you are teaching or using physics, please DO NOT use this definition for the velocity in one dimension (it’s a bad idea):
“Velocity = distance divided by time.”
OK, technically there are some cases where this would be fine — but it leads to the really terrible version of velocity that looks like this:
This is really wrong. Oh sure, it can sometimes give you the correct answer — but even a broken clock is right twice a day. I mean I see why people use this equation. If they use x for distance and t for time then it’s just the same thing as distance divided by time. It also has the correct units for velocity. But it’s still wrong.
The Best Definition
Let’s get to it. Here is the best definition of the velocity in one dimension (for an object moving along the x-axis).
First, I will point out the “avg” part of this. This equation is for the average velocity in the x-direction. If you have an object with a changing velocity (like a car with a rocket pushing it forward) then the velocity is not constant — but this equation still works as long as you realize it’s the average velocity.
Second, the important part of this is the Greek letter, Δ (Delta). We use this to mean “change in”. So, the average x-velocity is defined as the change in position (Δx) divided by the change in time (Δt). It’s all about change.
If you look at the position and velocity at the beginning and end of some time interval, then we can call the starting position x1 and the final position x2. Doing the same thing for time, you can write the average velocity as:
What does that equation look like? Yup, that looks like the slope of a line. If you plot x vs. y (like you often do in math), then the slope is defined as:
Using a Position-Time Graph
Well, let’s do it. Let’s make a graph. Here is a very simple position-vs-time graph for a car moving along with a constant velocity.
