The velocity of a particle is given by

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

v(t)=\begin{cases} 6 & 0\le t<2 \\ -3t+12 & 2\le t<6 \\ 2t-14 & 6\le t\le 9 \end{cases}

, with

v

in meters per second and

t

in seconds. If the particle’s position is

s(0)=0

, determine its position

s(9)

t=9\text{ s}