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).
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.
ABen did not change his speed at $11$11 am.
BBen increased his speed at $11$11 am.
CEvaluate 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.