Power Depends on Speed, Not Energy Gained

Steps:

• Gravitational potential energy (PE) gained equals mgh, where h is height; same stairs mean same h and m, so same PE for running or walking.
• Work done against gravity is identical in both cases, as it equals the PE change.
• Power is work done per unit time (P = W/t); running covers the height faster, reducing t.
• Thus, same work over less time means higher power for running.

Why C is correct:

• PE is mgh (independent of time), while power P = ΔPE/Δt increases for running due to shorter Δt.

Why the others are wrong:

• A: PE is the same, not more for running.
• B: PE is the same, and power is greater for running.
• D: Power is greater for running, not the same.

Final answer: C