Help with these please

For 0 S t S 6,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 v(t) = 2 sin(et/4) + 1. The acceleration of the 1 particle is given by a(t) = Eat/4 cos(et/4) 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. (d modied) For 0 S t S 6, the particle changes direction exactly once. Find the time when the particle changes direction. A particle moves along a straight line. For 0 S t S 5,the velocity of the particle is given by v(t) = 2 + (t2 + 306/5 t3,and the position of the particle is given by s(t). (a) Find all values of t in the interval 2 S t S 4 for which the speed ofthe particle is 2. (c) Find all times t in the interval 0 S t S 5 at which the particle changes direction. Justify your answer. Cd) 15 the speed of the particle increasing or decreasing at time t = 4-? Give a reason for your answer. For 0 S t S 12,a particle moves along the x axis. The velocity of the particle at time t is 1: given by 130:) = cos (at) . The particle is at position x = 2 at time t = 0. (a) For 0 S t S 12, when is the particle moving to the left? (c) Find the acceleration of the particle at time t. 15 the speed of the particle increasing, decreasing, or neither at time t = 4? Explain your reasoning