18. Motion with variable acceleration I

& v=\frac{ds}{dt} \\ & a=\frac{dv}{dt}=\frac{{{d}^{2}}s}{d{{t}^{2}}} \\ \end{align}

& \mathbf{r}=x\mathbf{i}+y\mathbf{j} \\ & \mathbf{v}=\frac{dx}{dt}\mathbf{i}+\frac{dy}{dt}\mathbf{j} \\ & \mathbf{a}=\frac{{{d}^{2}}x}{d{{t}^{2}}}\mathbf{i}+\frac{{{d}^{2}}y}{d{{t}^{2}}}\mathbf{j} \\ \end{align}