Part A

A cyclist is traveling on a flat straight road. His initial velocity is v_x = 10 m/s, and you can assume his displacement at this instant (t = 0 s) is 0 m. His acceleration is a_x = 0 m/s2 for the first 3 seconds. Between t = 3 s and t = 10 s, his velocity increases at a constant rate, and reaches v_x = 24 m/s at t = 10 s. Between t = 10 s and t = 15 s, his velocity decreases at a constant rate and reaches a value of v_x = 19 m/s at t = 15 s. His velocity then remains constant until t = 20 s.

1. Calculate the accelerations for the intervals 0-3 s, 3-10 s, 10-15s, 15-20s.

2. Plot a_x versus t.

3. Calculate the velocity changes in the intervals 0-3 s, 3-10 s, 10-15 s, and 15-20 s. This should agree with the values for speed given in the problem. Plot v_x versus t.

4. Calculate the displacement changes in the intervals 0-3 s, 3-10 s, 10-15 s, 15-20 s. Calculate the location of the cyclist at t = 0 s, t = 3 s, t = 10 s, t = 15 s, t = 20 s. Plot s_x versus t.

PART B

Shown on this graph is a plot of the vertical displacement of the center of gravity (c.g.) of a high jumper versus time (s_y versus t) during a typical jump. From this data, construct the following plots.

5. v_y versus t.

6. a_y versus t.

Do not be concerned if your values for v_y and a_y are exactly correct according to the slopes of the s_y versus t and v_y versus t graphs, respectively. I am only looking for two things in this problem: (a) that each graph has the correct shape, and (b) that the relative magnitudes of the velocity and acceleration values are correct.

Indicate the following features on the appropriate plot by marking the point or interval and labeling it with the number of each question.

7. The instant of the maximum vertical displacement of the c.g.

8. The instant of the maximum positive vertical velocity of the c.g. prior to takeoff.

9. The instant of the maximum negative vertical velocity of the c.g. prior to takeoff.

10. The interval where the velocity is changing at a constant rate.

11. The interval where the acceleration is equal to -9.81 m/s².