State Newton's second law of motion, derive F = ma and define the unit of force.

1. 1 · State the law in one line. The force acting on a body is directly proportional to the rate of change of its linear momentum, and acts in the direction of that change.
2. 2 · Set up the change in momentum. Mass m, initial velocity u, final velocity v, time t. Change in momentum = mv − mu.
3. 3 · Bring in acceleration. Rate of change = m(v − u)/t = ma, since a = (v − u)/t.
4. 4 · Reach F = ma. F ∝ ma, so F = kma. The unit of force is chosen so that k = 1. So F = ma.
5. 5 · Define the unit. 1 newton is the force that gives 1 kg an acceleration of 1 m s⁻². 1 N = 10⁵ dyne.
6. 6 · Real-life link. A loaded lorry needs a larger force than an empty one for the same acceleration.
7. 7 · Close in one line. So force = mass × acceleration, measured in newtons.

Scoring tip: Write every line of the derivation with symbols. The definition of 1 newton is an easy extra mark.