What is the formula for potential energy?

The formula for potential energy, specifically gravitational potential energy, is derived from the work done against gravity to elevate an object to a certain height. The formula is mass multiplied by gravity and the height from which the object is raised.

In this context, mass refers to the amount of matter in the object, gravity is the acceleration due to Earth's gravitational pull (approximately 9.81 m/s²), and height is the vertical distance from a reference point (usually ground level) to the position of the object. Therefore, when multiplying these three factors, you obtain the energy stored due to the position of the mass above the ground, which is crucial in many applications, such as calculating the energy stored in elevated water reservoirs or potential energy in various systems.

The other options provided involve different forms of energy or physical relationships. The formula involving 1/2 times mass times velocity squared relates to kinetic energy, which is the energy of motion, while mass times acceleration specifically describes Newton's second law and does not directly quantify energy. The term mass times velocity, while relevant in momentum calculations, also does not address energy directly. Hence, the choice that correctly identifies the formula for potential energy is mass times gravity times height.