Graphs

Question 1

Figure 2 is the displacement–time graph of a sprinter who sprints
100 m in 10 s, rests for 20 s, and then runs back to the starting
point in the next 30 s.
Using the graph, calculate the sprinter’s average velocity:
a in the first 10 seconds
b from t = 30 s to t = 60 s

Answer 1

a The sprinter’s average velocity in the first 10 seconds is the
gradient of the line over that time.
From the displacement–time graph, the gradient is given by:
vav = gradient = _
∆y
∆x
=
change in position _______________ time taken =
100 m − 0 m ____________
10 s − 0 s = 10 m s−1
The gradient of the line is constant for the first 10 seconds,
indicating that the velocity was also constant.
b From t = 30 s to t = 60 s, the average velocity can be
calculated: