Problem $2$

The cart below can roll without energy loss on the inclined board $($which has a varying angle $$ of

inclination, which is measured positive counter clockwise$).$ Suppose that the rate of change of the angle

$({}^{})$ is held constant at is $3\mathrm{.}3ra\frac{d}{s}$ and, at $t=0s,$ the initial conditions are given by:

$=\frac{}{6}$

$r=0\mathrm{.}7m$

$r^{}=0\frac{m}{s}$

During the first $0\mathrm{.}3$ s $,$ does the cart move up the ramp or down the ramp? $($Justify your answer,

quantitatively.$)$