How do I derive the accelleration of a particle with the work-energy theorem?

Question

I'm stumped...

Find the acceleration a of the particle:
Express the acceleration in terms of v_initial, v_final, and s.

s being the position displacement

Answer 1

Methinks you mean the work function, which is KE = W = Fs; where F is a force moving something along a distance s, which is called work (W) and is just another name for energy.

Thus KE = 1/2 mv^2 = mas; thus 1/2 v^2 = as and a = 1/2 v^2/s. Since work = W = 0 before we push with F, the initial velocity u = 0...nothing's moving. If we assume a constant force F, then the acceleration will be constant as well. Thus, a = (1/2) v^2/s is in terms of the final velocity (v) and the distance moved when v was reached.

Lesson learned: Acceleration in terms of velocity and distance does not depend on the particle mass m. That is, the acceleration is simply a kinematic relationship not relying on the physics that created the force.