State the work-energy theorem and prove it for a constant force. A 10 kg body moving at 4 m s⁻¹ is pushed by a 20 N force along its motion through 6 m. Find its final speed.

1. 1 · State the theorem. The work done by the net force on a body equals the change in its kinetic energy.
2. 2 · Set up. A constant force F gives mass m an acceleration a = F/m; its speed changes from v₁ to v₂ over a distance s.
3. 3 · Use an equation of motion. v₂² = v₁² + 2as, so a = (v₂² − v₁²)/2s.
4. 4 · Find the work. W = Fs = mas = ½m(v₂² − v₁²) = K₂ − K₁.
5. 5 · Solve the numerical.
   • W = 20 N × 6 m = 120 J; K₁ = ½ × 10 × 4² = 80 J.
   • K₂ = 80 + 120 = 200 J = ½ × 10 × v², so v² = 40.
   • v = √40 ≈ 6.3 m s⁻¹.
6. 6 · Real-life link. Brakes do negative work, which is why a faster car needs a much longer distance to stop.
7. 7 · Close in one line. So the work done on a body appears as a change in its kinetic energy.

Scoring tip: Write the equation of motion v₂² = v₁² + 2as before you substitute. In the numerical, find K₁ first: forgetting the starting kinetic energy is the usual slip.