The position vector of a particle at time t is given by r = 3cos(3t)i + 4sin(3t)j. Displacement is measured in meters and time is measured in seconds. Find an expression for the velocity of the particle at time t, hence find the speed when t = 3. Find an expression for the acceleration of the particle at time t, hence show that the acceleration is always directed towards the origin. The position vector of a second particle is r = -4sin(4t)i + 3cos(4t)j for 0 t 10. Find the time when the two particles are closest to each other.