A particle moves along a straight road. Its velocity as a function of time is described as follows:
• From t=0 to t=5s, its velocity remains constant at +4ms−1.
• From t=5s to t=9s, it decelerates uniformly and its velocity reaches −2ms−1 at t=9s.
• From t=9s to t=12s, it continues with the constant velocity of −2ms−1. The origin is at the starting point of the motion.
(i) Sketch the velocity–time graph for the entire motion, clearly indicating the numerical values on both axes.
(ii) Calculate the displacement of the particle for each of the three time intervals and hence obtain its net displacement at t=12s.
(iii) Determine the distance of the particle from the origin at t=12s.
(iv) Find the instant (if any) at which the particle returns to the origin during the interval 0 to 12s.