A hockey puck of mass M slides on a flat table lubricated with petroleum in the horizontal direction, exerting a drag force proportional to the cubic root of velocity, i.e. F_Dr = -cv^1/3 on the puck. If at t = 0, we know that v = v', find x and v as functions of time.

$v=\(\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}-\(\frac{2ct}{3M}\]\right\))^{\(\frac\)32};$ $x=\(\left\)(-\(\frac{3M}{5c}\]\right\))\(\left\[\lbrack\]\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}-\(\left\)(\(\frac{2ct}{3M}\[\right\))\(\right\))^{\(\frac\)52}-\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)53}\(\right\]\rbrack\)$

$v=\(\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}-\(\frac{2ct}{3M}\]\right\))^{\(\frac\)32};$ $x=\(\left\)(-\(\frac{3M}{5c}\]\right\))\(\left\[\lbrack\]\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}-\(\left\)(\(\frac{2ct}{3M}\[\right\))\(\right\))^{\(\frac\)52}\(\right\]\rbrack\)$

$v=\(\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}+\(\frac{2ct}{3M}\]\right\))^{\(\frac\)32};$ $x=\(\left\)(-\(\frac{3M}{5c}\]\right\))\(\left\[\lbrack\]\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}-\(\left\)(\(\frac{2ct}{3M}\[\right\))\(\right\))^{\(\frac\)52}\(\right\]\rbrack\)$

$v=\(\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}-\(\frac{2ct}{3M}\]\right\))^{\(\frac\)32};$ $x=\(\left\)(-\(\frac{M}{c}\]\right\))\(\left\[\lbrack\]\left\)(\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)23}-\(\left\)(\(\frac{2ct}{3M}\[\right\))\(\right\))^{\(\frac\)52}-\(\left\)(v^{\(\prime\)}\(\right\))^{\(\frac\)53}\(\right\]\rbrack\)$