A cyclist starts from rest, accelerates uniformly for a short time, rides with constant speed, and finally brakes to a stop. The detailed description is as follows:
• From t = 0 to t = 4 s the velocity rises uniformly to 8 m/s.
• From t = 4 s to t = 7 s the velocity remains constant.
• From t = 7 s to t = 9 s the cyclist slows down uniformly to rest.
Answer the following questions.
(i) Sketch a velocity–time graph for the entire 9 s journey and label the axes, the numerical values of velocity, and the three key instants t = 4 s, 7 s, and 9 s.
(ii) Explain briefly why each segment of your graph is straight, horizontal, or sloping downward.
(iii) Identify the intervals during which the acceleration is zero and during which it is negative, giving reasons from the graph.