Question 12.12: If a = 3t² i + cos2tj, find (a) da/dt     (b) |da/dt|      ......

(a) If \mathbf{a}=3 t^2 \mathbf{i}+\cos 2 t \mathbf{j}, then differentiation with respect to t yields

(b) \left|\frac{\mathrm{d} \mathbf{a}}{\mathrm{d} t}\right|=\sqrt{(6 t)^2+(-2 \sin 2 t)^2}=\sqrt{36 t^2+4 \sin ^2 2 t}

(c) \frac{\mathrm{d}^2 \mathbf{a}}{\mathrm{d} t^2}=6 \mathbf{i}-4 \cos 2 t \mathbf{j}