Work-energy theorem: net work equals change in kinetic energy

Steps:

• Compute final KE: $\frac{1}{2} \times 4 \times (1.5)^2 = 4.5$ J (initial KE is 0).
• Net work done: $(F - 1) \times 1.0 = 4.5$ J.
• Solve for F: $F - 1 = 4.5$, so $F = 5.5$ N.
• Matches choice D.

Why D is correct:

• Work-energy theorem states net work equals ΔKE; here, friction reduces net force, yielding F = 5.5 N.

Why the others are wrong:

• A: Underestimates net force, giving KE ≈ 1 J.
• B: Yields KE ≈ 2.5 J, below actual 4.5 J.
• C: Gives KE ≈ 3 J, still insufficient.

Final answer: D