In distance–time graphs (Figs. 2.10 to 2.13), distance is on the vertical ( y) axis and time is on the horizontal (x) axis. The slope of the graph gives the speed or velocity of the object. This comes from the formula for the graph’s slope:
Slope of a distance–time graph m =
y2 – y1
________ x2 – x1
m = slope (velocity, m s–1), y2 = end point (m), y1 = starting point (m), x2 = final time (s), x1 = initial time (s)
From this formula you can see that, by substituting in the x and y values, you are working out the change in distance travelled as time passes – that is, the velocity.
Examples of distance–time graphs 30
10 5 0
0 FIG. 2.10
In Fig. 2.10, the object starts from 0 m and moves with constant velocity for 15 s. It then stays at rest 10 m from the starting point for the next 25 s.
15
Time ( s)
40
5 0
025 Time ( s) FIG. 2.12
In Fig. 2.12, the object starts 5 m from the origin and moves with constant velocity for 25 s until it is 30 m away. This means it travels 25 m in 25 s. So its average velocity is 1 m s–1.
Time (s) FIG. 2.11
In Fig. 2.11, the object does not move and stays at rest the whole time.
FIG. 2.13
In Fig. 2.13, the object begins away from the origin. As time passes, it travels back to the originating point, slowing as it does so.
