A 500 g particle starts from rest under the force-versus-position graph shown. Find its speeds at x=8 m and x=12 m (nearly).

Question

G1 Physics · Accepted Answer

Step 1 — Principle: Work equals the signed area under the force–displacement graph; use W = ΔK = ½mv² - K₀. Step 2 — Working: The positive areas up to x = 8 m are 20×5 J and 10×3 J. Thus W₀₋₈ = 130 J. Step 3 — Working: As the 0.5 kg particle starts from rest, v₈ = √(2×130/0.5) = √520 ≈ 22.8 m s⁻¹. Step 4 — Working: From x = 8 m to x = 12 m, include the signed areas below as well as above the x-axis. Applying the work–energy theorem over the complete interval gives v₁₂ ≈ 20.6 m s⁻¹. Correct answ…