Deriving the work-energy theorem

[badman]

In this problem, you will use your prior knowledge to derive one of the most important relationships in mechanics: the work-energy theorem. We will start with a special case: a particle of mass m moving in the x direction at constant acceleration a. During a certain interval of time, the particle accelerates from v_initial to v_final, undergoing displacement s given by s=x_{\rm final}-x_{\rm initial}.


the problems asks me to find the acceleration :Find the acceleration a of the particle.
Express the acceleration in terms of v_initial, v_final, and s.
this is my answer: (v_final-v_initial)^2/s

but it says that: Your answer is close. One problem with your answer is that it is always positive, but acceleration can also be negative. ?

 

[StatusX]

Look at the units, and remember acceleration is the change in velocity per unit time.

 

[Doc Al]

Your answer is incorrect. Show how you arrived at it.