Question

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

Answer 1

The acceleration of the particle at t = π/2 is -1.

Step-by-step explanation:

To find the acceleration of the particle at t = π/2, we need to take the second derivative of the position function x(t) = (1/2)sin(t)cos(2t) with respect to time. First, let's find the first derivative: x'(t) = (1/2)cos(t)cos(2t) - sin(t)sin(2t). Now, taking the second derivative: x''(t) = -(1/2)sin(t)cos(2t) + (1/2)cos(t)sin(2t) - cos(t)cos(2t) - sin(t)sin(2t). Plugging in t = π/2, we get: x''(π/2) = -1.