Dependence of the coordinate of a point on time x = 8t – t ^ 2 (all values are in SI).

Dependence of the coordinate of a point on time x = 8t – t ^ 2 (all values are in SI). At what point in time is the speed of a point equal to -2 m / s?

These problems: the dependence of the coordinates of the point under consideration on time x = 8t – t ^ 2; V (required speed of the considered point) = -2 m / s.

1) Let us determine the dependence according to which the speed of the point under consideration changes: V = x ‘= (8t – t ^ 2)’ = 1 * 8 – 2 * t = 8 – 2t.

2) Determine the moment in time when the point reaches the required speed: -2 = 8 – 2t; 2t = 10 and t = 10/2 = 5 s.

Answer: The point in question will reach a speed of 2 m / s in 5 seconds.