Newtonian Mechanics

$ x(t) = 0 \quad \frac{dx}{dt} = 0 \quad \frac{d^2x}{dt^2} = 0 $

$ x(t) = 5t \quad \frac{dx}{dt} = 5 \quad \frac{d^2x}{dt^2} = 0 $

$ s(t) = t^2 \quad \frac{ds}{dx} = 2t \quad \frac{d^2s}{dx^2} = 2 $