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Graphs of Physical Phenomena


Distance-time graphs are a way to describe the movement of people or objects. They usually describe a trip that leaves and returns to a point (like a home base).

The vertical axis of a distance-time graph is the distance travelled from a starting point and the horizontal axis is the time taken from the starting point. In most graphs that depict time, time is on the horizontal ($x$x) axis.  


Reading a Distance-Time Graph

There are certain important features of a distance-time graph that we can use to interpret the journey being described. 

  • As the line moves away from the $x$x-axis, the object is moving further away from the "home" point.
  • As the line moves back towards the $x$x-axis, the object is returning home.
  • When the line is horizontal, the object is not moving.
  • The steeper the line, the greater the speed of the an object (ie. the faster it moves).
  • A straight line indicates a steady speed.
  • The total distance of the trip is the distance away from and returning home.

Now let's look at some worked examples working with distance-time graphs. 


Worked Examples

Question 1

Ben travels forwards and backwards along a straight line.

The graph shows Ben's distance from his starting point at various times of the day.

A line graph is displayed with the horizontal axis labeled "Time" marked from 9 to 5 in one-hour increments, and the vertical axis labeled "Distance (km)" marked from 0 to 300 in increments of 50. A line connects several points on the graph, starting at $\left(9,0\right)$(9,0), to $\left(11,150\right)$(11,150), to $\left(1,250\right)$(1,250), to $\left(2,250\right)$(2,250), to $\left(3,100\right)$(3,100), and ending at $\left(4,0\right)$(4,0).

  1. When did Ben start his journey?

  2. How far did Ben travel by $11$11 am?

  3. What happened to Ben's speed at $11$11 am?

    Ben decreased his speed at $11$11 am.


    Ben did not change his speed at $11$11 am.


    Ben increased his speed at $11$11 am.

  4. Evaluate Ben's speed between $11$11 am and $1$1 pm.

  5. What distance did Ben travel between $1$1 pm and $2$2 pm?

  6. What is the furthest distance travelled from the starting point?

  7. What is the total distance travelled by Ben from $9$9 am to $4$4 pm?

Question 2

Which graph shows the height of a ball being thrown vertically into the air?

  1. A






What if it's not a distance?

These ideas are easily extended into other areas.  So imagine if we replaced distance with height, volume or depth.  


  • As the line moves away from the x-axis, then the object is getting taller, more full or deeper. 
  • As the line moves back towards the x-axis, the object is getting shorter, less full or shallower.
  • When the line is horizontal, the objects depth, height, volume (or whatever is being measured on the y-axis) is not changing.
  • The steeper the line, the greater the change of the y-axis measurement.  
  • A straight line indicates a steady change of the y-axis measurement.

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