Ace A Level Physics 2025 – Power Up Your Physics Prowess!

The formula for calculating the energy stored in a spring indeed involves the relationship between force and displacement. The correct formula is given by \( E = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the extension or compression of the spring from its equilibrium position.

When considering the options provided, the first choice can be interpreted in the context of Hooke's Law, which states that the force exerted by a spring is proportional to its extension (F = kx). When a spring is stretched or compressed, the work done on it to change its length results in stored potential energy. The work done (which equals the energy stored) is calculated as the integral of force with respect to displacement.

Another way to understand the first choice is through the concept of an average force. The average force while stretching a spring from 0 to \( \Delta L \) is \( \frac{F}{2} \) (where \( F \) is the force applied at maximum extension). The work done against this average force when moving from the equilibrium position to the extension \( \Delta L \) contributes to the potential energy stored in the spring, hence arriving at \(