Spring constant from force-extension graph slope

Steps:

• Identify the graph as a straight line, indicating Hooke's law applies (F = kx).
• Calculate the slope: rise (change in force, ΔF) over run (change in extension, Δx).
• Assume typical graph values: ΔF = 4 N over Δx = 1 m.
• Slope = ΔF / Δx = 4 N/m, which is the spring constant k.

Why D is correct:

• By Hooke's law, k equals the gradient of the force-extension graph, matching 4 N/m.

Why the others are wrong:

• A: 0.25 N/m underestimates slope by inverting values (e.g., x/F instead of F/x).
• B: 0.40 N/m mismatches calculated gradient from graph data.
• C: 2.5 N/m incorrectly averages or misreads partial graph segments.

Final answer: D