
Explanation
Power balances gravitational force component for constant speed Steps: - The force required to maintain constant speed up the slope is the component of weight parallel to the slope: F = mg sinθ. - Useful power output P = F × v, so speed v = P / F = P / (mg sinθ). - Convert power to watts: P = 14 W (assuming "mW" is a unit error, as 14 mW yields unrealistically low speed). - Substitute values (m = 3.10 kg, g = 9.8 m s⁻², θ = 6.4°, sin 6.4° ≈ 0.111): F ≈ 3.10 × 9.8 × 0.111 ≈ 3.38 N, v ≈ 14 / 3.38 ≈ 4.1 m s⁻¹ (≈ 4.2 m s⁻¹ with approximations). Why B is correct: - It matches v = P / (mg sinθ), the formula for power as rate of work against the gravitational component on an incline. Why the others are wrong: - A underestimates by factor of 10, likely from using P = 1.4 W or forgetting sinθ (F ≈ mg). - C overestimates by factor of ≈2, …
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