Motion Graphs
There are three main motion graphs that tend to be studied in kinematics: displacement-time graphs, velocity-time graphs, and acceleration-time graphs. Displacement is a lot like distance - to be exact, it's how far you are from your starting position. Velocity is like speed, but with a direction. For example, 5 miles per hour is a speed, 5 miles per hour north is a velocity. And acceleration is the rate at which the velocity is changing.
Here is an example of a Displacement-Time graph:
It shows an object moving at a constant speed away from its starting position, and then slowing down to a stop.
To plot a velocity-time graph of this motion, we can either think conceptually about what's happening, or find the slope of the displacement-time graph. The slope of the displacement-time graph tells you the velocity. A Velocity-Time graph of the same motion looks like this:
We see a constant velocity at first, and then the object slows down to a stop. Or in other words, we have a positive velocity where the slope of the displacement graph was positive, and a velocity decreasing to zero where the slope of the displacement graph was flattening off to zero.
Now, to move on to an acceleration-time graph we can do the same thing again - think about how the velocity is changing conceptually, or find the slope of the velocity-time graph. The slope of the velocity-time graph tells you the acceleration. And an Acceleration-Time graph of the same motion looks like this:
