Answer
When $t = 0$:
$a = 0$
When $t = 1.0~s$:
$a = -0.872~cm/s^2$
When $t = 2.0~s$:
$a = -1.23~cm/s^2$
Work Step by Step
$y = (2.0~cm)~sin~(\frac{\pi t}{4})$
$v = (2.0~cm)(\frac{\pi}{4})~cos~(\frac{\pi t}{4})$
$a = -(2.0~cm)(\frac{\pi}{4})^2~sin~(\frac{\pi t}{4})$
When $t = 0$:
$a = -(2.0~cm)(\frac{\pi}{4})^2~sin~(\frac{\pi t}{4})$
$a = -(2.0~cm)(\frac{\pi}{4})^2~sin~[\frac{(\pi)(0)}{4}]$
$a = -(2.0~cm)(\frac{\pi}{4})^2~(0)$
$a = 0$
When $t = 1.0~s$:
$a = -(2.0~cm)(\frac{\pi}{4})^2~sin~(\frac{\pi t}{4})$
$a = -(2.0~cm)(\frac{\pi}{4})^2~sin~[\frac{(\pi)(1.0)}{4}]$
$a = -(2.0~cm)(\frac{\pi}{4})^2~(\frac{\sqrt{2}}{2})$
$a = -0.872~cm/s^2$
When $t = 2.0~s$:
$a = -(2.0~cm)(\frac{\pi}{4})^2~sin~(\frac{\pi t}{4})$
$a = -(2.0~cm)(\frac{\pi}{4})^2~sin~[\frac{(\pi)(2.0)}{4}]$
$a = -(2.0~cm)(\frac{\pi}{4})^2~(1)$
$a = -1.23~cm/s^2$
