Required information

Problem $11\mathrm{.}004-$ Railroad car

A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot bumper system. After the coupling, the motion of the car is defined by the relation $x=60e^{-4\mathrm{.}8t}sin16t,$ where $x$ and $t$ are expressed in millimeters and seconds, respectively.

$V_K$

Problem $11\mathrm{.}004.$a $-$ Railroad car

Determine the position, velocity, and acceleration of the railroad car when $t=0s.$

The position, velocity, and acceleration of the railroad car when $t=0s$ are

mm $,$

$m\frac{m}{s},$ and $m\frac{m}{s^2}$ respectively. $($Include a minus sign if necessary.$)$

Problem $11\mathrm{.}018-$ Magnets: position$-$dependent acceleration

A brass $($nonmagnetic$)$ block A and a steel magnet $B$ are in equilibrium in a brass tube under the magnetic repelling force of another steel magnet $C$ located at a distance $x=0\mathrm{.}005m$ from $B.$ The force is inversely proportional to the square of the distance between $B$ and $C.$ If block $A$ is suddenly removed, the acceleration of block $B$ is $a=-9\mathrm{.}81+\frac{k}{x^2},$ where a and $x$ are expressed in $\frac{m}{s^2}$ and meters, respectively, and $k=4{10}^{-4}\frac{m^3}{s^2}.$ Determine the maximum velocity and acceleration of $B.$

The maximum velocity is $q,m\frac{m}{s}$uarr.

The maximum acceleration is $q,\frac{m}{s^2}$uarr.