A particle starts from rest at t=0 and undergoes an acceleration as shown in figure.
Draw the velocity-time graph of the motion of the particle during the interval from zero to 4 second.

Explanation

It follows from figure that between t = 0 to t = 2s, the acceleration of the particle is `a = +3" m/s"^(2)`. Since the particle starts from rest, u = 0. Therefore, the velocity of the particle during the time interval t = 0 and t = 2 is given by
v = u + at = 0 + 3t = 3t
Thus the velocity at t = 1 sec. is 3 m/s and at t = 2 s, the velocity is 6 m/s. During the time interval t = 3 s and t = 4 s, the initial velocity u = 6 m/s and acceleration is `a = – 3 m//s^(2)`. Hence, during this time interval, the velocity of the particle is
v . = u + at . = 6 – 3t .
where t . = t – 2. Thus the velocity of the particle at t . = 1s or t = 3s is (6 – 3) = 3 m/s and t . = 2s or t = 4s, its velocity is (6 – 6) = 0.
These result can be tabulated as follows:
Time (s) 0 1 2 3 4
Velocity (m/s) 0 3 6 3 0
Figure shows the velocity-time graph of the motion