The specified displacement is
[tex]x(t)=(0.50\,m)cos( \frac{ \pi t}{3} )[/tex]
The velocity is the derivative f displacement with respect to time.
The velocity is
[tex]v(t)=-0.50( \frac{ \pi }{3} )sin( \frac{ \pi t}{3} )[/tex]
The maximum valu of v occurs when the sine functin is 1 or -1.
Therefore, the maximum velocity is
vmax = 0.5(π/3) = 0.524 m/s
Answer: 0.524 m/s
