Dimensional analysis matches energy to work

Steps:

• Energy has SI units kg·m²·s⁻² (joule, J).
• Force has units kg·m·s⁻² (newton, N); × distance (m) gives kg·m²·s⁻² for A.
• Power has units kg·m²·s⁻³ (watt, W = J/s); × time (s) gives kg·m²·s⁻² for B.
• Momentum has units kg·m·s⁻¹; × time (s) gives kg·m for C; × distance (m) gives kg·m²·s⁻¹ for D.

Why A is correct:

• Force × distance defines work (W = F·d), and work equals transferred energy per the work-energy theorem.

Why the others are wrong:

• B: Power × time equals energy (E = P·t), so units match, but A is the base mechanical expression.
• C: Gives units of impulse (change in momentum).
• D: Gives units of action (like in Hamilton's principle).

Final answer: A