Interpreting a Displacement Vs Time Graph (advanced)

Let's take a look at an advanced (curve) displacement vs time graph:

Notice that once again the TYPE of graph tells us helpful/interesting information:

  • The graph is a displacement vs time graph
  • The slope of a displacement vs time graph is velocity

The SHAPE of the graph tells us even more helpful information

  • As before, a positive slope on a graph of displacement vs time shows positive velocity (in this case towards the east)
  • As before, a negative slope on a graph of displacement vs time shows negative velocity (in this case towards the opposite direction from east, which is velocity to the west)
  • Notice that in this instance the object's velocity is constantly changing so there is no flat slope.

The fact that the graph is a curve is also significant. A curve tells us that the object's velocity is itself changing (since the slope of a curve is changing).

A curve with an increasing slope tells us that the object's velocity is increasing.

A curve with a decreasing slope tells us that the object's velocity is decreasing.

  • Since the slope is changing, we can find the slope at two different places on that graph to get two different velocities. With two different velocities occurring over two different times we can calculate the acceleration that object experiences between those times using our definition of acceleration:

a = ∆v/∆t

(vf - vi)/(tf - ti)

 

THE OPPOSITE MOTION: A bike riding back up the hill

As before, we can analyze the graph above and get a lot of information BEFORE we even work with the actual numbers:

An initial analysis of the graph above shows that:

Between zero and 7 seconds:

  • The object's velocity is decreasing (the line is curved downward with a negative slope) therefore the object is experiencing negative acceleration.
  • The object is moving in a negative direction (to the west) during that time (the slope is negative). We know that because the displacement is decreasing with time.
  • The object's velocity is decreasing to zero)