A particle moves along the x-axis such that its displacement x varies with time t as follows:
Segment AB: 0≤t≤4s, x increases uniformly from 0 to 12m.
Segment BC: 4≤t≤7s, x=12+3(t−4)2.
Segment CD: 7≤t≤8s, x remains constant at its value at t=7s.
(a) Draw a rough sketch of the position–time graph for the complete motion, clearly marking the three segments.
(b) Determine the average velocity of the particle during each of the three segments.
(c) Find the instantaneous velocity at t=5s.
(d) Comment on the nature of acceleration in each segment, stating whether it is zero, constant, or varying.