The point moves in a circle with a radius of r = 16 m according to the equation s = 4t ^ 2.

The point moves in a circle with a radius of r = 16 m according to the equation s = 4t ^ 2. At what point in time is the normal acceleration an = 0.64 m / s2

Data: r – radius of the circle (r = 16 m); S – equation of motion of a point (S = 4t ^ 2); an is the required normal acceleration (an = 0.64 m / s2).

1) The equation for changing the speed of the specified point: V = S ‘= (4t ^ 2)’ = 4 * 2 * t = 8t.

2) The sought moment in time: an = V ^ 2 / r = 8 ^ 2 * t ^ 2 / r, whence we express: t = √ (r * an / 8 ^ 2) = √ (16 * 0.64 / 8 ^ 2) = 0.4 s.

Answer: The specified point will move with a normal acceleration of 0.64 m / s2 0.4 s after the start of the movement.