A \(2.0-\mathrm{kg}\) cart and a \(3.0-\mathrm{kg}\) cart collide on a low-friction track. The \(3.0-\mathrm{kg}\) cart is initially moving at \(1.0 \mathrm{~m} / \mathrm{s}\) to the right, but after the collision it is moving at \(5.0 \mathrm{~m} / \mathrm{s}\) to the right. After the collision, the \(2.0-\mathrm{kg}\) cart is moving to the right at \(3.0 \mathrm{~m} / \mathrm{s}\).

(a) What was the \(2.0-\mathrm{kg}\) cart's initial velocity?

(b) What would your answer be if, other quantities being unchanged, the \(3.0-\mathrm{kg}\) cart were initially moving to the left at \(1.0 \mathrm{~m} / \mathrm{s}\) ?