GCSE · Physics · AQA · Spec 8463
Newton's Second Law (F = m a)
Push the same object harder and it accelerates more. Give the same push to a heavier object and it accelerates less.
Change one thing — watch acceleration respond
Same mass: 2 N resultant → 1 m/s².
First hold mass fixed. Then hold resultant force fixed.
F = m × a
F is the RESULTANT force.
Tap the quantity you want to find. The triangle shows you the formula.
Cover resultant force, mass or acceleration to reveal its rearranged formula, then plug in numbers to solve.
Apply F = ma
Problem
Work two Newton's-second-law calculations, keeping 'resultant force' explicit.
Physics · Investigation
Investigate force, mass and acceleration
How do resultant force and mass affect acceleration?
PredictWhich pattern should the results show?
Resultant force (N)
Mass (kg)
Change resultant force and mass separately, then compare the acceleration. The scene is deliberately generic: compare the authored force, mass and acceleration readings.
AQA Required Practical 7 · Acceleration
Inertial mass
Problem
A resultant force of 6 N produces an acceleration of 2 m/s². Use the force-to-acceleration ratio to find the inertial mass.
AQA Higher tier only.
Equations you need
Taken directly from the exam-board specification.
F = resultant force (N) · m = mass (kg) · a = acceleration (m/s^2)
Learn it — you must recall this in the exam
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
What you need to know
- The force in F = m a is the resultant force on the object.
- At constant mass: double the resultant force → double the acceleration.
- At constant resultant force: double the mass → halve the acceleration.
- Use F = m a with F in N, m in kg and a in m/s².
- AQA Required Practical 7 investigates acceleration against resultant force at constant mass and acceleration against mass at constant force.
- AQA Higher: inertial mass = force ÷ acceleration and describes how difficult it is to change an object's velocity.
The big picture
Newton's Second Law links an object's acceleration to the resultant force on it and to its mass. At constant mass, acceleration is directly proportional to resultant force; at constant resultant force, acceleration is inversely proportional to mass. The relationship is F = m a, with F as the resultant force in newtons, m in kilograms and a in metres per second squared.
Key points
Worked example
Problem
A 6.0 kg trolley has a resultant force of 18 N acting on it. Calculate its acceleration. Then state what the acceleration would be if the same resultant force acted on a 12 kg trolley.
⚠ Watch out
Using one force from the diagram instead of the resultant force. Newton's Second Law uses the single overall resultant acting on the object; it is not a Newton's Third Law force pair.
★ Exam tip
For AQA Physics, F = m a is a recall-and-apply equation. In a calculation, make sure F is the resultant force. For RP7 questions, keep one variable constant while changing the other.
Memory hook
Think F over m: acceleration follows the push of the resultant force, but mass resists the change. Bigger F → bigger a; bigger m → smaller a.
Check yourself
A 3.0 kg object has a resultant force of 12 N. What is its acceleration? What would its acceleration be if the mass were 6.0 kg but the resultant force stayed at 12 N?
Flashcards
(14)How does acceleration change when resultant force increases while mass stays constant?
How does acceleration change when mass increases while resultant force stays constant?
What equation links resultant force, mass and acceleration?
What does F mean in F = m a?
What are the units of mass and acceleration in F = m a?
At constant mass, the resultant force doubles. What happens to the acceleration?
At constant resultant force, the mass doubles. What happens to the acceleration?
A 4 kg object accelerates at 3 m/s². What resultant force acts on it?
A resultant force of 20 N acts on a 5 kg object. What is its acceleration?
A 10 N force acts right and a 4 N force acts left on a 3 kg object. What is its acceleration?
What is inertial mass?
How is inertial mass calculated from force and acceleration?
What relationship is investigated in AQA Physics required practical 7?
For AQA Physics, how is F = m a classified in this packet?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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