The inequality at the top of page 99 in <A HREF="http://www.math.tifr.res.in/~publ/ln/tifr01.pdf">Lectures on
The Riemann Zeta–Function</A> gives
$$|\zeta(\tfrac{1}{2}+it)|<9t^{1/2},\;\;t\geq 1.$$
To cover the whole the interval $t\geq 0$, just add $3/2$ to the right-hand-side of the inequality.