Answer
When $t = 0$:
$v = 1.57~cm/s$
When $t = 1.0~s$:
$v = 1.11~cm/s$
When $t = 2.0~s$:
$v = 0$
Work Step by Step
$y = (2.0~cm)~sin~(\frac{\pi t}{4})$
$v = (2.0~cm)(\frac{\pi}{4})~cos~(\frac{\pi t}{4})$
When $t = 0$:
$v = (2.0~cm)(\frac{\pi}{4})~cos~(\frac{\pi t}{4})$
$v = (2.0~cm)(\frac{\pi}{4})~cos~[\frac{(\pi) (0)}{4}]$
$v = (2.0~cm)(\frac{\pi}{4})~(1)$
$v = \frac{\pi}{2}~cm/s$
$v = 1.57~cm/s$
When $t = 1.0~s$:
$v = (2.0~cm)(\frac{\pi}{4})~cos~(\frac{\pi t}{4})$
$v = (2.0~cm)(\frac{\pi}{4})~cos~[\frac{(\pi) (1.0)}{4}]$
$v = (2.0~cm)(\frac{\pi}{4})~(\frac{\sqrt{2}}{2})$
$v = 1.11~cm/s$
When $t = 2.0~s$:
$v = (2.0~cm)(\frac{\pi}{4})~cos~(\frac{\pi t}{4})$
$v = (2.0~cm)(\frac{\pi}{4})~cos~[\frac{(\pi) (2.0)}{4}]$
$v = (2.0~cm)(\frac{\pi}{4})~(0)$
$v = 0$
