Determine the projection onto the OX axis of the force under which the x coordinate of a body weighing

Determine the projection onto the OX axis of the force under which the x coordinate of a body weighing m = 4 kg changes according to the law x = At + Bt², where A = 3 m / s, B = 0.2 m / s².

According to Newton’s second law, the projection onto the Ox axis of the resultant force F = ma, where m = 4 kg is the body mass, a is the projection onto the Ox axis of the body’s acceleration. We find the projection on the axis Oх of the body’s acceleration from the condition that the x coordinate of the body changes according to the law x = At ​​+ Bt ^ ², where A = 3 m / s, B = 0.2 m / s². To do this, we will use the general formula of the body motion equation: x = x (start) + v (start) ∙ t + (a / 2) ∙ t ^ ², where x (start) is the initial coordinate of the body, v (start) is the projection of the velocity on Ox at the beginning of the movement a is the projection of the body’s acceleration onto the Ox axis. Comparing this equation with what is given in the problem statement, we get: a / 2 = B, then a = 2 ∙ B = 2 ∙ 0.2 = 0.4 (m / s ^ ²).
F = 4 ∙ 0.4 = 1.6 (H).
Answer: 1.6 N.