Find the velocity … and speed … and tangent vector … for…

Find the velocity $\mathbf{v}$ and speed $|\mathbf{v}|$ and tangent vector $\mathbf{T}$ for these motions: (a) $\mathbf{R}=t\mathbf{i}+t^2\mathbf{j}$ (b) $\mathbf{R}=t\cos t\mathbf{i}+t\sin t\mathbf{j}$ (c) $\mathbf{R}=(t+1)\mathbf{i}+(2t+1)\mathbf{j}+(2t+2)\mathbf{k}$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.1 The Position Vector, #19