Numerically solving a differential equation up to a certain value of the time dependent variable

I have a second order differential equation

x''(t) = f(x)

with an initial condition x(0) = x0 ; x'(0) = 0; I wish to find the t value for which x(t) = 0;

Currently I am using ode45 to solve this (expressing it as two coupled linear odes) for some time range and linearly interpolating the solution between the two points where x changes sign. Given that I also have the gradient at this points it's fairly easy to fit a cubic spline but this really isn't accurate, there must be a better way of obtaining this solution! Doesn't anyone know how to go about this?