y′(t) = f(t) (but not a function of y)

y′(t) = −(9.8\frac{m}{s^{2}} ) t + v_{0}

y_{i+1} = y_{i} + y′_{i} dt

y_{i+1} = y_{i} + \frac{1}{2}(y′_{i} + y′_{i+1}) dt

y_{i+1} = y_{i} + \frac{(y′_{i} + 4y′_{i+1/2} + y′_{i+1})}{6} dt