Name the three types of graphs. Give examples of the same with labelled diagrams.
Answers
position-time
Let's begin by graphing some examples of motion at a constant velocity. Three different curves are included on the graph to the right, each with an initial position of zero. Note first that the graphs are all straight. (Any kind of line drawn on a graph is called a curve. Even a straight line is called a curve in mathematics.) This is to be expected given the linear nature of the appropriate equation. (The independent variable of a linear function is raised no higher than the first power.)
velocity-time
The most important thing to remember about velocity-time graphs is that they are velocity-time graphs, not position-time graphs. There is something about a line graph that makes people think they're looking at the path of an object. A common beginner's mistake is to look at the graph to the right and think that the the v = 9.0 m/s line corresponds to an object that is "higher" than the other objects. Don't think like this. It's wrong.
acceleration-time
The acceleration-time graph of any object traveling with a constant velocity is the same. This is true regardless of the velocity of the object. An airplane flying at a constant 270 m/s (600 mph), a sloth walking with a constant speed 0.4 m/s (1 mph), and a couch potato lying motionless in front of the TV for hours will all have the same acceleration-time graphs — a horizontal line collinear with the horizontal axis. That's because the velocity of each of these objects is constant. They're not accelerating. Their accelerations are zero. As with velocity-time graphs, the important thing to remember is that the height above the horizontal axis doesn't correspond to position or velocity, it corresponds to acceleration.
