Deriving KE from kinematic equations and work principle

Steps:

• Start with work done by net force: W = F × s = ma × s (constant acceleration).
• Use equation 2 (v = u + at) to express a = (v - u)/t.
• Substitute into equation 3 (s = (u + v)t/2) to get as = (v - u)(u + v)/2 = (v² - u²)/2.
• Thus, W = m(v² - u²)/2 = ½mv² - ½mu², defining KE = ½mv² (equation 1 confirms the velocity relation).

Why A is correct:

• Equations 1, 2, and 3 are the core kinematic relations that combine to yield the velocity-displacement link needed for the work-energy theorem, deriving ΔKE = W.

Why the others are wrong:

• B: Lacks equations 2 and 3; equation 4 (momentum) is unrelated to energy derivation.
• C: Excludes equation 2; momentum (4) doesn't provide acceleration-time relation.
• D: Omits equation 1; momentum (4) isn't kinematic and can't derive velocity-squared term.

Final answer: A