Newton’s second law and momentum change

What you will learn

Favg = (mv−mu)/t; F = ma for constant mass; vector resultants.

Specification mapping: B2.5, B2.5.1

Prerequisites: B2.4, B1.3.6

Physical principles

Newton’s second law relates resultant external force to the rate of change of momentum. Over a finite interval, average resultant force is Δp/Δt. For constant mass this becomes Favg = m(v−u)/Δt; if acceleration is constant, F = ma. Use the resultant, not one arbitrary force in isolation.

Force is proportional to acceleration when mass is fixed and inversely related to the time needed for a specified momentum change. The relation F = ma is vectorial: acceleration points along the resultant force. If forward drive and backward resistance both act, subtract them before using the mass.

A short impact often has varying force. Δp/Δt gives average force, not automatically the peak. An impulse is the momentum change and equals the area under the force–time graph. The constant-mass form is suitable for ordinary vehicle and object problems here; systems shedding significant mass need more careful modelling.

Scientific diagram and interpretation

Equations and relationships

Favg = (mv−mu)/t; F = ma

Worked examples and applications

Common misconceptions

An impact-force calculation from total momentum change gives an average unless the force is constant.

Examination technique

Draw the free-body diagram, find the vector resultant and then apply the law.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.