Show that the work done on a body at rest to give it a speed v is ½mv². A 1200 kg car speeds up from 10 m s⁻¹ to 20 m s⁻¹. Find the work done by its engine, ignoring friction.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · State the idea. Work done on a body changes its kinetic energy.
2 · Set up. A force F acts on a mass m at rest and moves it through a distance s, giving it speed v.
3 · Derive.
W = F × s and F = ma
v² = u² + 2as with u = 0 gives s = v²/2a
W = ma × v²/2a = ½mv²
4 · Apply it to the car.
Initial KE = ½ × 1200 × 10² = 60 000 J
Final KE = ½ × 1200 × 20² = 240 000 J
Work = 240 000 − 60 000 = 180 000 J
5 · Real-life link. Doubling a car's speed needs four times the kinetic energy. So fast driving burns more fuel and needs longer braking distances.
6 · Close. So the engine does 1.8 × 10⁵ J of work.
Scoring tip: Write the three linking equations (W = Fs, F = ma, v² = u² + 2as) before combining them. Use final KE minus initial KE for the numerical.
