A boat moves along a straight section of river so that its velocity relative to the riverbank at time t seconds is
v(t)=t2−6t+5(0≤t≤6).
Positive velocity indicates motion in the positive x-direction; negative velocity indicates motion in the opposite direction.
(a) Determine the boat’s displacement over the time interval [0,6] seconds. Show all work leading to your result.
(b) Compute the total distance traveled by the boat on the same interval.
(c) Find the ratio ∣displacement∣distance traveled and express it in simplest exact form.
(d) Explain what the value of the ratio in part (c) indicates about the boat’s motion during the interval.