Find the speed of a point moving in a straight line according to the law s = -2cos2t at time t = n / 6s.

The movement of the body is determined by the function S = -2cos2t:

To find the velocity of a body from the function S (t) = -2cos2t, it is necessary to take the derivative (derivative of the first order) from this function:

x (t) ‘= S’ = V = (-2cos2t) ‘= – 2 * 2 * (-sin2t) = 4sin2t.

At the time t = Π / 6, the speed of the point is: V = 4sin (2Π / 6) = 4sin (Π / 3) = 4 * √3 / 2 = 2 * √3 ≈ 3.46.

Answer: The point speed is 3.46.