At time t t\,t seconds, where t≥0t \ge 0t≥0, a particle P P\,P has acceleration a=[(3t−3)i+(2t−4)j]\mathbf{a} = \left[(3t - 3)\mathbf{i} + (2t - 4)\mathbf{j}\right]a=[(3t−3)i+(2t−4)j] m s−2^{-2}−2.
Initially P P\,P has velocity (−4i+4j)(-4\mathbf{i} + 4\mathbf{j})(−4i+4j) m s−1^{-1}−1.
Show that the velocity of P P\,P is v=(32t2−3t−4)i+(t2−4t+4)j\mathbf{v}=\left(\dfrac{3}{2}t^2-3t-4\right)\mathbf{i}+\left(t^2-4t+4\right)\mathbf{j}v=(23t2−3t−4)i+(t2−4t+4)j m s−1^{-1}−1.
Find the velocity of P P\,P at each of the two times when P P\,P is moving parallel to the vector (2i+j)(2\mathbf{i} + \mathbf{j})(2i+j).