A trolley of mass 5kg rests on a long, horizontal track. The track is smooth except for one rough section. The trolley experiences the following sequence of events:
Stage I (t=0 to t=1s): A constant horizontal force pushes the trolley.
Stage II (t=1s to t=4s): The pushing force is removed while the trolley continues on the smooth track.
Stage III (t=4s to t=5s): The trolley enters the rough section where an equal but opposite horizontal force acts on it.
Stage IV (t>5s): The trolley leaves the rough section onto a smooth track again, with no horizontal forces acting.
a. (i) For each stage, state whether the net external horizontal force on the trolley is zero or non-zero, and specify its direction wherever applicable.
b. (ii) For each stage, describe qualitatively (increase, constant, decrease) the acceleration and velocity of the trolley.
c. (iii) On a single set of axes, sketch a qualitative (not to scale) velocity–time graph for the entire motion from t=0s to t=8s.
d. (iv) Explain the features of your graph in part (iii) by applying Newton’s first law of motion to each stage.