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In contrast to the previous examples, let's graph the position of an object with a constant, non-zero acceleration starting from rest at the origin.

when two curves coincide, the two objects have the same position at that time.

the "y" intercept is the initial position.

The height of a curve tells you nothing about its slope. Note that the initial position being zero does not necessarily imply that the initial velocity is also zero. If it were a race, then the contestants were already moving when the race began, since each curve has a non-zero slope at the start. This graph could represent a race of some sort where the contestants were all lined up at the starting line (although, at these speeds it must have been a race between tortoises). Since each of these graphs has its intercept at the origin, each of these objects had the same initial position. Thus velocity corresponds to slope and initial position to the intercept on the vertical axis (commonly thought of as the "y" axis). (The independent variable of a linear function is raised no higher than the first power.)Ĭompare the position-time equation for constant velocity with the classic slope-intercept equation taught in introductory algebra. Even a straight line is called a curve in mathematics.) This is to be expected given the linear nature of the appropriate equation. (Any kind of line drawn on a graph is called a curve. Note first that the graphs are all straight.

Three different curves are included on the graph to the right, each with an initial position of zero. Let's begin by graphing some examples of motion at a constant velocity. Graphs of motion come in several types depending on which of the kinematic quantities (time, position, velocity, acceleration) are assigned to which axis. Graphs are often the best way to convey descriptions of real world events in a compact form. Sometimes you need a picture to show what's going on - a mathematical picture called a graph. Since, as I rightly pointed out, "no object has ever traveled in a straight line with constant acceleration anywhere in the universe at any time" these equations are only approximately true, only once in a while.Įquations are great for describing idealized situations, but they don't always cut it. You should recall that the three (or four) equations presented in that section were only valid for motion with constant acceleration along a straight line. Think back to the previous section on the equations of motion. When it comes to depth, nothing beats an equation. All of these relationships can now be written in a single equation. Galileo's description of an object moving with constant speed (perhaps the first application of mathematics to motion) required one definition, four axioms, and six theorems. Equations can easily contain the information equivalent of several sentences. Modern mathematical notation is a highly compact way to encode ideas.