Interpreting a Displacement Vs Time Graph (basic)

Let's take a look at a basic (straight line) displacement vs time graph:

Notice that 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

  • A positive slope on a graph of displacement vs time shows positive velocity (in this case towards the east)
  • 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)
  • A flat slope shows displacement isn't changing which yields a slope of zero. Since slope = velocity that means the velocity of the object is zero when the slope is zero.

Whether the graph is a line or 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 straight line tells us that the object's velocity is constant

 

THEREFORE:

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 5 seconds:

  • The object's velocity is constant (the line is straight with a positive slope).
  • The object is moving in a positive direction (to the east) during that time (the slope is positive)

Between 5 seconds and 8 seconds:

  • The object's velocity is constant (the line is straight).
  • The object's velocity is zero (the line is horizontal so displacement isn't changing)

Between 8 seconds and 13 seconds:

  • The object's velocity is constant (the line is straight).
  • The object is moving in a negative direction (opposite to the east which is west) during that time (the slope is negative)

NOTICE that there is NO transition time for the object to slow down, speed up or stop.

That is truly impossible in the REAL world (except perhaps in quantum mechanics, but I digress), but in physics, we frequently use such basic situations to help us understand basic physics concepts.