

Definition of kinetic energy: the work done to
accelerate an object from rest to its current velocity. Assumptions: Constant net force and constant acceleration from kinematics:
but v_{o }= 0 , so
from Newton's second Law:
substitution into the kinematic equations yields:
solving for time gives:
substituting into the displacement equation gives:
However, displacement x Force = Work, so:
but by definition W = K so

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