A white rectangle of width U and height V with a smaller grey rectangle outside of width delta U and height V

This white rectangle has a fixed height, \(v\), and its width \(u\) varies as a function of time, \(t\). We can write the rate of change of the width as \(\dfrac{du}{dt}\) or \(\dot{u}\). You can think of this as the speed at which the right hand edge is moving.

Our rectangle has height \(v=\quantity{3}{cm}\) and width \(u=\quantity{\left(\frac{1}{2}t^2+1\right)}{cm}\) at time \(\quantity{t}{s}\).

What is the rate of change of area, \(\dfrac{dA}{dt}\), at

  1. \(t=0\)?

  2. \(t=3\)?