Using graphs to interpret motion.

Graphs are a good way to convey descriptions of real world events in a compact form. Graphs of motion come in differing types depending on what they are describing.  They are used with some measurable or calculable value on the y axis (displacement, velocity or acceleration) and time on the x axis.

Lets start with a displacement time graph


Between C & D, the object has not changed is position and so we can assume its not moving.  

Between B & C the displacement away from the start is increasing at a uniform rate so we can assume it is happening at a constant velocity.

Between A & B the displacement away from the start is increasing at a non uniform rate, so we can assume that object is accelerating away.

Between D & E the object is moving again.  But how?  In what direction compared to the line BC?  How do you know this?




Velocity time graphs.



In this case, the object is changing velocity in a positive manner, therefore it is accelerating.  After 10 seconds it moves at a constant velocity for a further 5 seconds.  After 15 seconds it begins to slow until it is stationary at 30 second.  Between 30 and 40 seconds, it is moving with negative velocity, and accelerating backwards compared to the original motion.  After 40 seconds is slows down again and stops at 55 seconds.


Recall that in Maths when graphing:

                    rise
Slope =      _______
                    run


and 



                    displacement
velocity =   ______________
                         time

Therefore the slope of the line can be used to calculate velocity. 

One of the benefits of a velocity time graph is that the area under it is the displacement.  So if you can calculate the areas of triangles, rectangles and squares, you'll be fine at this stage.  Be warned; if you are doing Mathematics or higher, you'll have to calculate the area under curves.




Here are a couple of summing up graphs:
1. Displacement vs time





2. Velocity vs time.