At time t t\,t seconds, where t≥0t \ge 0t≥0, a particle P P\,P moves so that its acceleration is a=[(1−2t)i+(5−t2)j]\mathbf{a} = \left[(1 - 2t)\mathbf{i} + (5 - t^2)\mathbf{j}\right]a=[(1−2t)i+(5−t2)j] m s−2^{-2}−2.
At the instant when t=0t = 0t=0, the velocity of P P\,P is 20i20\mathbf{i}20i m s−1^{-1}−1.
Find the velocity of P P\,P when t=4t = 4t=4.
Find the value of t t\,t at the instant when P P\,P is moving in a direction perpendicular to i\mathbf{i}i.