Question

A particle starts from rest at time t = 0 and undergoes acceleration a, as shown in the Figure. 

(i) Draw a neat sketch showing the velocity of the particle as a function of time during the interval 1 to 4 seconds, indicating each second on the abscissa. 

(ii) Draw a neat sketch showing the displacement of the particle as a function of time during 0 to 2 second. In both the cases, explain the various steps.  

Answer 1

Area under the a-t graph in the given time interval is equal to the change in velocity of the particle in the given time interval. Thus v-t graph can be plotted if the initial velocity is known. Area under the v-t graph in the given time interval is equal to the displacement of the particle in the given time interval.

(i) The velocity is given by the area enclosed during the time interval; and the velocity is constant from 0 to 2 sec.

(ii) The particle starts from rest, and the acceleration a is constant from 0 to 2 sec.

Beyond t = 4s, the acceleration becomes negative, the curvature of the graph becomes opposite at this instant. In the interval between t = 2s and t = 3s,