The arc length function for a curve $ y = f(x) $, where $ f $ is an increasing function, is $ s(x) = \int_0^x \sqrt{3t + 5}\ dt $.
(a) If $ f $ has y-intercept 2, find an equation for $ f $.
(b) What point on the graph of $ f $ is 3 units along the curve from the y-intercept? State your answer rounded to 3 decimal places.