# Discussion leading to Newton's second law

Students will have discovered that:

• a constant force accelerates a given mass with constant acceleration;
• doubling the force doubles the acceleration, i.e. the acceleration is directly proportional to the force for a given mass. F is proportional to a
• the force, F, needed for a given acceleration is inversely proportional to the mass, m
• for a given force, F, the acceleration, a, is inversely proportional to the mass,m

(many students find inverse proportion a problem).

Considering these points together leads to F is proportional to ma or F = a constant x ma.

Mass is measured in kg and acceleration in m/s/s but what of force? If the constant is equated to unity, then we are defining a unit of force. In the SI system the force is measured in newtons (symbol N), leading to F = ma.

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