Graphs of Physical Phenomena

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 ($x$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).

When did Ben start his journey?
How far did Ben travel by $11$11 am?
What happened to Ben's speed at $11$11 am?
Ben decreased his speed at $11$11 am.
A
Ben did not change his speed at $11$11 am.
B
Ben increased his speed at $11$11 am.
C
Evaluate Ben's speed between $11$11 am and $1$1 pm.
What distance did Ben travel between $1$1 pm and $2$2 pm?
What is the furthest distance travelled from the starting point?
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?

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.