Consider the velocity function for an object moving along a line (see figure).

a. Describe the motion of the object over the interval [0, 6]. 

b. Use geometry to find the displacement of the object between t = 0 and t = 3.

c. Use geometry to find the displacement of the object between t = 3 and t = 5.

d. Assuming that the velocity remains 30 m/s, for t ≥ 4, find the function that gives the displacement between t = 0 and any time t ≥ 5.

3 4 5 Time (s) Velocity (m/s)