A boat moves along a straight section of river so that its velocity relative to the…

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A boat moves along a straight section of river so that its velocity relative to the riverbank at time

t

seconds is

v(t)=t^{2}-6t+5 \quad (0\le t\le 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

\dfrac{\text{distance traveled}}{|\text{displacement}|}

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.