The body moves according to the law s = 18t + 9t ^ 2-t ^ 3 Find the maximum speed.

Given the problem: the law according to which a given body moves: S (t) = 18t + 9t ^ 2 – t ^ 3.

1) The law of speed change: V (t) = S (t) ‘= (18t + 9t ^ 2 – t ^ 3)’ = (18 * 1 + 9 * 2t – 3 * t ^ 2) = 18 + 18t – 3t ^ 2 = – 3t ^ 2 + 18t + 18.

2) The graph of the obtained law of speed (quadratic function) of a given body is a parabola.

3) Since the leading coefficient of the obtained quadratic function is negative, the time when the body has maximum speed corresponds to the x coordinate of the parabola vertex: x = t = -b / 2a = -18 / (2 * (-3)) = 3 s.

4) Maximum speed: Vmax = – 3 * 32 + 18 * 3 + 18 = 45 m / s.