A particle moves along a straight line so that its velocity (in ) at time seconds is…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle moves along a straight line so that its velocity

v

(in

\text{m/s}

) at time

t

seconds is given by

v(t)=\begin{cases}6t-9, & 0\le t\le 2,\ ^2-4t+3, & 2<t\le 6.\end{cases}

The particle's position is

s(0)=5\text{ m}

. (a) Determine the particle's position

s(6)

. (b) Calculate the particle's average velocity on the interval

0\le t\le 6

and state the units. (c) Show that there exists a time

c

(0,6)

at which the instantaneous velocity equals the average velocity found in part (b). Find one such value of

c

. (d) Interpret the result of part (c) in terms of the motion of the particle.