The body moves according to the law s = 2t + 0.45t ^ 2-0.1t ^ 3. At what point in time will the body

The body moves according to the law s = 2t + 0.45t ^ 2-0.1t ^ 3. At what point in time will the body velocity module take its maximum value?

Data: the law of motion of a body: S (t) = 2t + 0.45t ^ 2 – 0.1t ^ 3.

1) The law of speed change: V (t) = S (t) ‘= (2t + 0.45t ^ 2 – 0.1t ^ 3)’ = (2 * 1 + 0.45 * 2t – 0.1 * 3 * t ^ 2) = 2 + 0.9t – 0.3t ^ 2 = -0.3t ^ 2 + 0.9t + 2 (corresponds to a quadratic function; the graph is a parabola; since the leading coefficient of the resulting quadratic function is negative, the branches parabolas are directed downward).

2) The time when the moving body has maximum speed (x coordinate of the parabola): x = t = -b / 2a = -0.9 / (2 * (-0.3)) = 1.5 s.

Answer:  the body speed module is maximum at t = 1.5 s.