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.
There are certain important features of a distance-time graph that we can use to interpret the journey being described.
Now let's look at some worked examples working with distance-time graphs.
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.
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?
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?
Which graph shows the height of a ball being thrown vertically into the air?
These ideas are easily extended into other areas. So imagine if we replaced distance with height, volume or depth.
Describe a situation that would explain the events illustrated by a given graph of a relationship between two variables