A car travels along a straight highway. Its velocity v(t), measured in meters per second, changes with time t (seconds) as follows:
• From t = 0 to t = 4, v(t) increases linearly from 0 m/s to 20 m/s.
• From t = 4 to t = 10, v(t) remains constant at 20 m/s.
• From t = 10 to t = 14, v(t) decreases linearly from 20 m/s to 0 m/s.
Assume the velocity varies exactly as described on each interval.
(a) Describe on which time intervals the car’s acceleration is positive, zero, or negative, and justify your answer in terms of the behaviour of v(t).
(b) Compute the numerical value of the acceleration (including units) for 0 ≤ t ≤ 4 and for 10 ≤ t ≤ 14.
(c) Explain the physical significance of the acceleration being zero during 4 ≤ t ≤ 10.
(d) Sketch a qualitative graph of acceleration a(t) versus time t on the interval 0 ≤ t ≤ 14, clearly indicating key values and features.