Problem $11\mathrm{.}090-$ Analyze the motion of a particle given

position in rectangular components as functions of $t$

The motion of a vibrating particle is defined by the position

vector $r=10(1-e^{-3t})i+(4e^{-2t}sin15t)j,$ where $r$ and $t$ are

expressed in millimeters and seconds, respectively.

Problem $11\mathrm{.}090.$b $-$ Analyze the

motion of a particle given

position in rectangular

components as functions of $t-$

velocity and acceleration

Determine the velocity and acceleration

when $t=0\mathrm{.}5s.($Round the velocity

value to three decimal places.$)$

When $t=0\mathrm{.}5s,$ the velocity is

$m\frac{m}{s}36\mathrm{.}2$ and the acceleration is

$1m\frac{m}{s^2}$