Graphs of motion can be used to analyze motion. Graphical solutions yield identical solutions to mathematical methods for deriving motion equations. The slope of a graph of displacement x vs. time t i...Graphs of motion can be used to analyze motion. Graphical solutions yield identical solutions to mathematical methods for deriving motion equations. The slope of a graph of displacement x vs. time t is velocity v. The slope of a graph of velocity v vs. time t graph is acceleration a. Average velocity, instantaneous velocity, and acceleration can all be obtained by analyzing graphs.