Motion Diagrams

Motion diagrams are a graphical description of an object in motion.  In general they will consist of a position graph, a velocity graph, and possibly an acceleration graph for the time period(s) of interest.  These graphs are qualitative; they do not need to be numerically exact, but they should show the general trends of the motion, including whether it is moving positively or negatively, etc.  If there is more than one moving object, you will need a set for each object.
Steps for making a motion diagram:
  1. Draw axis for a velocity graph.  If it is not specified in the problem, decide what is the positive direction.  It can be a good idea to make a note on your sketch.  Then draw a velocity graph, paying attention to whether you are moving in the positive or negative direction (above or below the axis) and whether you are speeding up (away from the axis), slowing down (towards the axis) or constant velocity (horizontal line).  If the motion is complex, such as speeding up and then moving at constant velocity, draw the graph so that the different time segments are clearly distinguished.
  2. If the velocity graph is not a constant horizontal line, draw the acceleration graph by noting what the slope of the velocity graph is in each time segment present.  Check that the sign of acceleration you get from this is same as the acceleration you expect in the problem.  If not, check your work.  Line the graphs up so that each time segment is lined up with the same segment on the velocity graph.
  3. Draw the position graph axis and determine where on it you are starting (near, far away, negative, etc.).  Use the magnitude of the velocity graph at a particular point to determine whether the position is increasing or decreasing, and whether it is fast or slow.  If there are different time segments, line them up with the other graphs.
Constant Right
Constant Left
Speeding up Right
Speeding up Left
Away and back