A glider on an air track moves only along the +x direction. Its velocity as a function of time is given verbally below.
• From t = 0 s to t = 3 s, the velocity increases uniformly from 0 m/s to 6 m/s.
• From t = 3 s to t = 5 s, the velocity remains constant at 6 m/s.
• From t = 5 s to t = 7 s, the velocity decreases uniformly to –2 m/s.
• At t = 7 s the velocity instantaneously becomes 0 m/s and stays zero until t = 9 s.
The glider’s initial position is x = 0 m at t = 0 s.
(a) Determine the glider’s total displacement from t = 0 s to t = 7 s. Show how you obtained the value from the velocity description.
(b) On axes of your own, sketch a position–time graph covering the interval t = 0 s to t = 9 s. Accurately indicate the glider’s position at t = 3 s, 5 s, and 7 s.
(c) On a separate set of axes, sketch the corresponding acceleration–time graph for 0 s ≤ t ≤ 9 s. Label all non-zero acceleration values numerically.
(d) Calculate the glider’s average speed for the interval 0 s ≤ t ≤ 7 s and explain how your answer is consistent with the graphs you produced.