Deriving KE from work-energy principle

Steps:

• Work done W = F s, and KE gained equals W.
• Apply Newton's second law: F = m a, so W = m a s.
• Use kinematic equation with initial velocity u = 0: v² = 2 a s, so a s = v² / 2.
• Substitute: W = m (v² / 2) = ½ m v², yielding KE formula.

Why C is correct:

• ½ m v² is the target formula being derived, not a prerequisite equation.

Why the others are wrong:

• A: F = m a links force to acceleration, essential for substituting into work.
• B: W = F s defines work done, directly used as starting point.
• D: v² = u² + 2 a s relates velocity, acceleration, and displacement, needed to solve for a s.

Final answer: C