8 3. (i) At time t seconds, where t  0 , a particle P moves so that its acceleration a m s−2 is given by a = (1 − 4t) i + (3 − t2) j At the instant when t = 0, the velocity of P is 36i m s−1 (a) Find the velocity of P when t = 4 (3) (b) Find the value of t at the instant when P is moving in a direction perpendicular to i (3) (ii) At time t seconds, where t  0 , a particle Q moves so that its position vector r metres, relative to a fixed origin O, is given by r = (t2 − t) i + 3t j Find the value of t at the instant when the speed of Q is 5 m s−1 (6) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________