Question

The following data were collected during a short race between

two friends.

Velocity (m/s) 0 0.5 1 1.5 2 2 4 6 2 0

Time (s) 0 2 4 6 8 10 12 14 16 18

a) Describe the different sections of the graph.

b) Determine the acceleration over the first eight seconds.

c) Determine the maximum acceleration.

d) Using the graph calculate the displacement:

i) over the first eight seconds

ii) the total race.

e) Find the maximum velocity reached by the runner.

Answer 1

a) We have accelerated motion (0 to 8 s), uniform motion (8 to 10 s), more accelerated (10 to 14), decelerated (14 to 16), a bit less decelerated (16 to 18).

b) The acceleration is

$$a=\frac vt=0.25\text{ m/s}^2.$$

c) The maximum:

$$a=\frac vt=2\text{ m/s}^2.$$

d) Displacement:

$$d(8)=8·2/2=8\text{ m}.\\ d_{18}=38\text{ m}.$$

e) Max. velocity:

$$v_\text{max}=v(14)=6\text{ m/s}.$$