Question

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

Answer 1

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