A \(2.34-\mathrm{kg}\) cart on a long, level, low-friction track is heading for a small electric fan at \(0.23 \mathrm{~m} / \mathrm{s}\). The fan, which was initially off, is turned on. As the fan speeds up, the magnitude of the force it exerts on the cart is given by \(a t^{2}\), where \(a=0.0200 \mathrm{~N} / \mathrm{s}^{2}\). What is the speed of the cart \(3.5 \mathrm{~s}\) after the fan is turned on? After how many seconds is the cart's velocity zero?