(e) P’s motion can be indicated as shown in Figure N4–15. P moves to the right
if t < 1, reverses its direction at t = 1, moves to the left when 1 < t < 2,
reverses again at t = 2, and continues to the right for all t > 2. The position of
P at certain times t are shown in the following table:
Thus P travels a total of 34 units between times t = 0 and t = 4.
Example 27 __
Answer the questions of Example 26 if the law of motion is
s = t 4 − 4t 3.SOLUTION: Since v = 4 t^3 − 12 t^2 = 4 t^2 (t − 3) and a = 12 t^2 − 24 t = 12 t(t − 2), the
signs of v and a are as follows: