Power balances resistive force times velocity at maximum speed Steps:

• At maximum speed, net force is zero, so driving force equals resistive force kv.
• Maximum power P equals driving force times speed: P = (kv) × v.
• Simplify: P = k v².
• Solve for v: v = (P / k)^{1/2}.

Why C is correct:

• It follows from the power formula P = F v, where F = kv at constant maximum speed.

Why the others are wrong:

• A: Applies only if resistive force is constant (independent of v), but here F = kv.
• B: Correctly states v² = P / k but does not solve for v as the other options do.
• D: Would apply if resistive force were proportional to v³ (P = k v⁴), which is not the case.

Final answer: C