12 4. A particle P moves on the x-axis. At time t seconds, t  0 , P is x metres from the origin O and moving with velocity v m s−1 in the direction of x increasing, where v = 5 sin 2t When t = 0 , x = 1 and P is at rest. (a) Find the magnitude and direction of the acceleration of P at the instant when P is next at rest. (4) (b) Show that 1  x  6 (4) (c) Find the total time, in the first 4π seconds of the motion, for which P is more than 3 metres from O (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________