The question:

When you use a sewing-machine, the needle moves in relation to the sewing plate (where the clothe is). To the time t, the needle's height y(t) over the sewing-plate is decided by:

$\displaystyle y(t)=\frac 32 \cdot sin(12\pi t)$

Where t is meazured in seconds and y(t) is meazured in centimeters.

The needle's velocity to the time t is y'(t). What is the velocity of the needle when it passes the sewing-plate?

I found the y'(t) previously with the help from you guys:

$\displaystyle y'(t)=\frac 32 \cdot 12 \pi \cdot \cos(12 \pi t)$

But what now? I'm a bit lost.