A student cannot remember whether the energy stored in a stretched spring is 1/2kx or 1/2kx², where…

Step 1. $\frac{1}{2}kx$. $[\text{M}\,\text{T}^{-2}][\text{L}] = [\text{M}\,\text{L}\,\text{T}^{-2}]$: a force, not an energy.

Step 2. $\frac{1}{2}kx^2$. $[\text{M}\,\text{T}^{-2}][\text{L}^2] = [\text{M}\,\text{L}^2\,\text{T}^{-2}]$: an energy. This is the one.

Step 3. (b). $\frac{1}{2} \times 250\ \text{N/m} \times (0.040\ \text{m})^2 = 0.20\ \text{J}$.