Answer
(a) A = 13 cm
(b) x = 9.2 cm
Work Step by Step
(a) We can find the angular frequency as:
$T = \frac{2\pi}{\omega}$
$\omega = \frac{2\pi}{T}$
$\omega = \frac{2\pi}{2.0~s}$
$\omega = \pi~rad/s$
We can find the amplitude as:
$v_{max} = A~\omega$
$A = \frac{v_{max}}{\omega}$
$A = \frac{0.40~m/s}{\pi~rad/s}$
$A = 0.13~m = 13~cm$
(b) We can find $x$ when $t = 0.25~s$;
$x(t) = A~cos(\omega~t)$
$x = (0.13~m)~cos[(\pi)(0.25~s)]$
$x = 0.092~m = 9.2~cm$
