Question

1. For 0 6, £ £t a particle is moving along the x-axis. The particle’s position, x t( ), is not explicitly given. The velocity of the particle is given by ( ) ( ) 4 2sin 1. t vt e = + The acceleration of the particle is given by ( ) ( ) 1 4 4 cos 2 t t at e e = and x( ) 0 2. = (a) Is the speed of the particle increasing or decreasing at time t = 5.5 ? Give a reason for your answer. (b) Find the average velocity of the particle for the time period 0 6. £ £t (c) Find the total distance traveled by the particle from time t = 0 to t = 6. (d) For 0 6, £ £t the particle changes direction exactly