A mass of \(\quantity{3}{kg}\) has position vector \(\mathbf{r} = (3t^2+2t)\mathbf{i}-4t^2\mathbf{j}\), where \(\mathbf{r}\) is measured in metres and \(t\) is the time in seconds.
Find its velocity and acceleration vectors in terms of \(t\).
Show that it is subject to a force of magnitude \(\quantity{30}{N}\), and find the direction of the force.
