Answer
$v = 0.377~m/s$
$a = -0.615~m/s^2$
Work Step by Step
We can find the angular frequency.
$T = \frac{2\pi}{\omega}$
$\omega = \frac{2\pi}{T}$
$\omega = \frac{2\pi}{3.20~s}$
$\omega = 1.96~rad/s$
We can find the speed when x = 0.160 m.
$v = \omega~\sqrt{A^2-x^2}$
$v = (1.96~rad/s)~\sqrt{(0.250~m)^2-(0.160~m)^2}$
$v = 0.377~m/s$
We can find the acceleration when x = 0.160 m.
$a = -\omega^2~x$
$a = -(1.96~rad/s)^2(0.160~m)$
$a = -0.615~m/s^2$
