The slope of the position versus time curve is the velocity. The object starts at x=0 with a constant positive velocity (and zero acceleration), and moves that way for 20 s. Then, until t = 30s, the positive curvature of the position graph means that the object has a positive acceleration. Its velocity increases. From 30 s to about 45 s, the position graph has a negative curvature. It slows down to rest, changes direction, and then starts moving in the negative direction, faster and faster. From 45 s to 50 s, the positive curvature of the position graph means that the object has a positive acceleration. It is still moving in the negative direction, but slows down (i.e., positive acceleration).
Work Step by Step
The graph is a representation of motion expressed as position over time. Each change in the line's slope signifies a specific pattern of movement.