Derivation of kinetic energy via work-energy theorem

Steps:

• Work done by net force equals change in kinetic energy: W = F s (option D).
• Newton's second law relates force to acceleration: F = m a (option A).
• Kinematic equation links final speed to initial speed, acceleration, and displacement: v² = u² + 2 a s (option C); for u=0, a s = v²/2.
• Substitute to get W = m (v²/2) = ½ m v², defining kinetic energy E.

Why B is correct:

• s = v t assumes constant velocity, but derivation requires acceleration for changing speed from rest.

Why the others are wrong:

• A: Directly used to express force in terms of mass and acceleration.
• C: Provides relation between acceleration, displacement, and speed change.
• D: Defines work as force times displacement, starting point of energy derivation.

Final answer: B