1. The problem statement, all variables and given/known data An object starts from rest at the origin and moves in the positive x direction. The velocity is proportional to the displacment. I am trying to find the equation linking velocity to displacement. 2. Relevant equations Since the object starts at rest and then moves in the positive direction, acceleration is non-zero. The chapter in the textbook concerns constant acceleration. So, I think v2= vi2+ 2a[x-xi] would be appropriate. vi is initial velocity and xi is initial displacement. 3. The attempt at a solution Setting both the initial velocity and initial displacement to zero gives v = sqrt(2ax). Does this count as velocity proportional to displacement? I found online this type of thing being referred to as proportional to the square root. Any help appreciated. Apologies for lack of latex. This isn't on a computer!