Answer to Question #275908 in Physics for Haile

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) 0-8s: acceleration

8-10 s: uniform motion

10-14: deceleration

14-16: deceleration

16-18: deceleration

(b) The acceleration is

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

(c) The maximum acceleration is:

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

(d) The displacement is:

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

(e) The maximum velocity:

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