A transverse wave on a string is described by the following wave function.

y $=$

$0\mathrm{.}105$ sin$$

$9$

x $+3$t

where x and y are in meters and t is in seconds.

$($a$)$ Determine the transverse speed at t $=0\mathrm{.}140$ s for an element of the string located at x $=1\mathrm{.}80$ m$.$

m$/$s

$($b$)$ Determine the transverse acceleration at t $=0\mathrm{.}140$ s for an element of the string located at x $=1\mathrm{.}80$ m$.$

Given the equation for the vertical position of elements of the string as a function of time, how do you determine the velocity of those elements as a function of time? m$/$s$2$