The motion of a particle along a straight line occurs in three successive stages:
• Stage I: It starts from rest and moves with a constant acceleration a1 for a time t1.
• Stage II: It then continues with the constant velocity attained at the end of Stage I for a further time t2.
• Stage III: Finally, it is brought to rest by a constant retardation a3 applied for a time t3.
Answer the following:
(i) Draw a qualitative velocity–time (v–t) graph for the entire motion, clearly marking the three time intervals.
(ii) Explain how the slope of each straight-line segment of the graph represents the magnitude and sign of the acceleration during that interval.
(iii) State the conditions that must be satisfied for the velocity and displacement of the particle at the instants t=t1 and t=t1+t2 so that the motion remains continuous.
(iv) Using only the information visible from your graph, describe how you would calculate the total displacement of the particle without directly using any kinematic equation.
a. (i) Draw a qualitative velocity–time graph.
b. (ii) Explain how the slope relates to acceleration in each stage.
c. (iii) State continuity conditions for velocity and displacement at the transition instants.
d. (iv) Describe a graphical method to obtain the total displacement.