1. The problem statement, all variables and given/known data a particle of mass accelerates at rest from the origin . The acceleration of the particle 'a' is given by a=k/(x+4)^4 , where x is the distance from the origin . given data : when x=5 , velocity 'v'=8 what is the maximum velocity that can be obtained ? 3. The attempt at a solution I even got stuck when I thought about it briefly. When the particle's velocity reaches maximum , the acceleration must be 0 , and either k=0 or x must be at infinity . After that , I have no idea what i can do about it . Shall I use definite integration (from 0 to infinity) or indefinite integration (which leaves the integration constant C )? what I am sure is merely that k has to be obtained by integration and the given numerical data.