The displacement (in feet) of a certain particle moving in a straight line is given by s = t3/6, where is measured in seconds.
(a) Find the average velocity over the following time periods:
(i) [1, 3] (ii) [1, 2]
(iii) [1, 1.5] (iv) [1, 1.1]
(b) Find the instantaneous velocity when t = 1.
(c) Draw the graph of as a function of and draw the secant lines whose slopes are the average velocities found in part (a).
(d) Draw the tangent line whose slope is the instantaneous velocity from part (b).