The particle moves along a curved trajectory with a constant modulus velocity V = 5m / s. find the radius

The particle moves along a curved trajectory with a constant modulus velocity V = 5m / s. find the radius of curvature R of the trajectory at the point at which the acceleration of the particle is a = 2m / s ^ 2.

To find the value of the radius of curvature of the trajectory on which the specified point is located, we apply the formula: a = ac = V ^ 2 / R, whence we express: R = V ^ 2 / a.

Variable values: V – constant speed of the specified point (V = 5 m / s); a – particle acceleration (a = 2 m / s2).

Calculation: R = V ^ 2 / a = 5 ^ 2/2 = 12.5 m.

Answer: the radius of curvature of the trajectory of the specified point is 12.5 m.