I already explained how they are roughly equivalent - kinetic energy converts to force when it is dissipated/transferred to a target. Bowling ball with kinetic energy strikes another bowling ball, exerting force (roughly equivalent to the kinetic energy it had) upon the second bowling ball. Second ball (assuming it is not too large, nor anchored) will now have new kinetic energy roughly equivalent to the force it received, minus any opposing factors (friction, elasticity, gravity, etc.).
And, yes, actually, accelleration does have something to do with kinetic energy, when you consider the entire sequence. It is accelerated to a given velocity (at which point it has kinetic energy based upon that velocity, mass, etc.). And force applied over time (which, in this case, is related to the distance available for acceleration) provides the acceleration that produces the velocity that's the variable (in the example) for the kinetic energy.
So, yeah, related.