A particle moves along the x-axis so that at any time t, its position is given by x (t) = 1/2 sint+cos (2t). What is the acceleration of the particle at t=pi/2

X (t) = 1/2sin t + cos (2t)

speed = x' (t) = 1/2cos t - 2sin (2t)

acceleration = x'' (t) = - 1/2sin t - 4cos (2t)

When t = pi/2,

acceleration = - 1/2sin (pi/2) - 4cos (pi) = - 1/2 - 4 (-1) = - 1/2 + 4 = 3 1/2 = 7/2 m/s^2