AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Newton’s laws of motion: F = ma for situations where the mass is constant.
When mass is constant, Newton’s second law becomes F = ma, where F is the resultant force in newtons, m is mass in kilograms and a is acceleration in metres per second squared.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 2
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When mass is constant, Newton’s second law becomes F = ma, where F is the resultant force in newtons, m is mass in kilograms and a is acceleration in metres per second squared. Use it to find any one quantity from the other two: a 1500 kg car with a resultant forward force of 3000 N accelerates at 2 m s⁻². Always find the resultant force by vector addition first, then substitute. The equation is vectorial, so acceleration is in the same direction as the resultant force. Rearranged forms a = F ÷ m and m = F ÷ a are equally valid. For motion on a slope, resolve weight into components parallel and perpendicular to the slope before applying F = ma along the direction of motion.
What earns the marks
- Identify F as the resultant force, found by adding all forces as vectors, not any single applied force.
- Substitute consistent SI units: newtons, kilograms and metres per second squared.
- Rearrange F = ma correctly to calculate acceleration or mass when required.
- Resolve forces on a slope or at an angle before applying F = ma along the chosen direction.
- Interpret a negative acceleration as deceleration or acceleration opposite to the chosen positive direction.
Common mistakes and how to put them right
Forgetting to subtract friction or drag from the driving force.
Put it right by calculating the resultant force first.
Mixing grams with kilograms or kilometres per hour with metres per second.
Put it right by converting to SI units before substitution.
Treating F = ma as valid when mass changes, such as a rocket burning fuel.
Put it right by using the momentum form for variable mass.
Exam tips
- Write the equation, rearrange symbolically, then substitute numbers to reduce arithmetic slips.
- State the direction of the resultant force and acceleration in your answer.
- For slope problems, show the resolved weight component before using F = ma.
Try the lesson
The start of the Newton’s laws of motion: F = ma for situations where the mass is constant. lesson, made from checked teaching notes for this specification point.
Have a go first
A resultant force of 12 N acts on a trolley of mass 4 kg. What is the acceleration of the trolley?
Listen
When mass is constant, Newton’s second law becomes F = ma, where F is the resultant force in newtons, m is mass in kilograms and a is acceleration in metres per second squared. Use it to find any one quantity from the other two: a 1500 kg car with a resultant forward force of 3000 N accelerates at 2 m s⁻². Always find the resultant force by vector addition first, then substitute. The equation is vectorial, so acceleration is in the same direction as the resultant force. Rearranged forms a = F ÷ m and m = F ÷ a are equally valid. For motion on a slope, resolve weight into components parallel and perpendicular to the slope before applying F = ma along the direction of motion. A strong answer earns marks for these points. Identify F as the resultant force, found by adding all forces as vectors, not any single applied force. Substitute consistent SI units: newtons, kilograms and metres per second squared. Rearrange F = ma correctly to calculate acceleration or mass when required. Resolve forces on a slope or at an angle before applying F = ma along the chosen direction. A common slip: Forgetting to subtract friction or drag from the driving force. Instead, calculating the resultant force first. Exam tip: Write the equation, rearrange symbolically, then substitute numbers to reduce arithmetic slips.
Key words
Say what each word means before you turn the card.
Resultant force
Try answering aloud or in your head before turning the card.
Acceleration
Try answering aloud or in your head before turning the card.
Constant mass
Try answering aloud or in your head before turning the card.
Vector direction
Try answering aloud or in your head before turning the card.
See every definition
- Resultant force
- Found by adding all forces as vectors, not any single applied force, and is the F in F = ma.
- Acceleration
- In metres per second squared, it is in the same direction as the resultant force because the equation is vectorial.
- Constant mass
- The condition under which Newton's second law becomes F = ma, so the momentum form is needed when mass changes.
- Vector direction
- Acceleration is in the same direction as the resultant force, and a negative acceleration is deceleration or acceleration opposite to the chosen positive direction.
There is more to this lesson
The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Test your understanding of Newton’s laws of motion: F = ma for situations where the mass is constant.
Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge