# Modeling ODE

**Calculus**Level 1

Suppose that we drop a stone, which falls freely with no air resistance. Experiments show that, under that assumption of negligible air resistance, the acceleration \( {y}^{\prime\prime}=\frac { {d}^{2}y }{ {d}^{2}t } \) of this motion is constant, i.e. equal to the so-called acceleration of gravity \(g=9.8 \text{ m/sec}^2.\) State this as an ordinary differential equation for \(y(t),\) the distance fallen as a function of time \(t.\)