8.1.4.18 Geometric and physical applications

Problem: The material point \( m \) moves linearly to the fixed centre, attracting it with a force inversely proportional to the cube of the distance from the centre (proportionality coefficient \( k>0 \) ). Find the law of motion, if it starts from a state of rest, when the point is at \( x_{0} \) distance from the centre. Determine the time after which the point will reach the centre.