Graphical Analysis of Motion

 First, it must be remembered that there are 3 different descriptions for motion  Constant position (at rest)  Constant velocity  Constant acceleration

 For constant position or at rest, the velocity and acceleration are both 0 because the object is not moving. Position is a horizontal line because there is no change in position.

 For constant velocity the acceleration is zero because the object is not accelerating. The velocity, being constant, is represented by a horizontal line. The position is then a non- horizontal linear graph because the object is moving.

 For constant acceleration the acceleration is a constant, obviously, so it is horizontal. The velocity then becomes linear because it is changing. The position-time graph then becomes quadratic, representing the non- constant speed of the object.

 Something that may help is thinking of DT, VT, and AT in terms of polynomials  The degree of a polynomial is basically a number that refers to its shape  0- constant (horizontal)  1- linear  2- quadratic  3- cubic

 So for an object at rest all 3 graphs would have a degree of zero because they are horizontal  For constant velocity, velocity would be 0 and position would become 1  For constant acceleration, acceleration would be 0, velocity would become 1, making position quadratic with a degree of 2  For any of these quantities, each quantity below it increases by one degree from the degree of the initial quantity

 One more thing to know is that the slope of each graph is equal to the value of the quantity above it (slope of VT = acceleration), while the area under a graph is equal to the value of the quantity preceding it (area under VT = position). It’s always helpful to keep this in mind.