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India
Class IX

Graphs of Physical Phenomena

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Lesson

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) 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 $$x-axis, the object is moving further away from the "home" point.
  • As the line moves back towards the $$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 <mi>coord(9, 0)</mi>, to <mi>coord(11, 150)</mi>, to <mi>coord(1, 250)</mi>, to <mi>coord(2, 250)</mi>, to <mi>coord(3, 100)</mi>, and ending at <mi>coord(4, 0)</mi>.

  1. When did Ben start his journey?

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

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

    Ben decreased his speed at $$11 am.

    A

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

    B

    Ben increased his speed at $$11 am.

    C

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

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

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

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

Question 2

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

  1. A

    B

    C

    D

 

 

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.  

Then, 

  • 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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