Newton's Second Law applied to resistive force

Steps:

• Assume first push F gives constant velocity (net force zero): F = R.
• Second push 2F gives acceleration a: net force 2F - R = m a.
• Substitute R = F: 2F - F = m a, so F = m a.
• Thus, resistive force R = F = m a.

Why A is correct:

• R = m a directly from balancing forces and Newton's second law F_net = m a.

Why the others are wrong:

• B. 2ma overestimates resistance, implying F = 3 m a for acceleration a.
• C. 3ma requires even larger applied force for same acceleration.
• D. 4ma mismatches the given force-acceleration relation.

Final answer: A