Newton's laws

Objective. Apply resultant force equals mass times acceleration.

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Learn: the key idea

Newton's laws of motion govern how forces affect objects: the first law states an object stays at rest or constant velocity unless acted on by a resultant force, the second law states resultant force equals mass times acceleration (F=ma), and the third law states forces occur in equal and opposite pairs. To use the second law, find the resultant force by adding all forces in a chosen direction, then divide by mass to find acceleration. For example, a 5kg object with resultant force 20N has acceleration a=F/m=20/5=4m/s². Always resolve all forces into one direction before applying F=ma.

Worked example

A resultant force of 15N acts on a 3kg object. Use Newton's laws to find the object's acceleration.

1 $Newton's second law states F=ma$
2 $Rearrange to find acceleration: a=F/m$
3 $a=15/3$
4 $a=5m/s²$

Answer: 5m/s²

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Common mistake. Students apply F=ma using only one force when multiple forces act, ignoring opposing forces like friction. Always find the resultant force by combining all forces before dividing by mass.

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