Newton's second law

The idea

$F = ma$ : the resultant force equals mass times acceleration. Find the resultant by adding the forces in the direction of motion and subtracting those against it.

Choose the direction of acceleration as positive.
Resultant $=$ forces with it $-$ forces against it.
Set the resultant equal to $ma$ and solve.

Watch out Use the resultant force, not just the biggest force.

See it worked

Worked example

A $4\text{ kg}$ box is pulled with $30\text{ N}$ against a resistance of $10\text{ N}$ . Find its acceleration.

Resultant: $30 - 10 = 20\text{ N}$ .
$20 = 4a$ .
$a = 5\text{ m s}^{-2}$ .

Answer $5\text{ m s}^{-2}$

Your turn

Question 1Non-calculator3 marks

A resultant force of $7\text{ N}$ acts on a $2\text{ kg}$ particle. Find its acceleration.

Question 2Non-calculator3 marks

A car of mass $1200\text{ kg}$ has a driving force of $3000\text{ N}$ and resistance $600\text{ N}$ . Find its acceleration.

Question 3Calculator allowed3 marks

A ball of mass $0.5\text{ kg}$ is lifted by a vertical force of $8\text{ N}$ . Find its acceleration. Use $g = 9.8\text{ m s}^{-2}$ .

In past papers

24 official questions in 19 papers since 2018. The latest:

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