16   5. At time t seconds, a particle P has velocity v m s−1, where v = 3t 1 2  i − 2t j        t > 0 (a) Find the acceleration of P at time t seconds, where t > 0 (2) (b) Find the value of t at the instant when P is moving in the direction of i − j (3) At time t seconds, where t > 0, the position vector of P, relative to a fixed origin O, is r metres. When t = 1, r = −j (c) Find an expression for r in terms of t. (3) (d) Find the exact distance of P from O at the instant when P is moving with speed 10 m s−1 (6) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________