AQA GCSE Combined Science Foundation (8464), Foundation tier · Physics › Forces › Forces and motion › Forces, accelerations and Newton's Laws of motion
Practise Newton's Second Law. 8 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Newton's Second Law links resultant force, mass and acceleration: F = m a. You need to use it in calculations, estimate forces in everyday road transport, and describe the required practical on force, mass and acceleration.
Key facts
F = m a (resultant force = mass × acceleration)
Units: F in N, m in kg, a in m/s2
a ∝ F (at constant mass)
a ∝ 1/m (at constant force)
Always use the RESULTANT force
Acceleration is in the direction of the resultant force
~ means 'approximately'; car mass ~1000 kg
Notes
The law
The acceleration of an object is proportional to the resultant force acting on it, and inversely proportional to its mass.
resultant force = mass × acceleration: F = m a
F in newtons (N), m in kilograms (kg), a in metres per second squared (m/s2).
The acceleration is in the same direction as the resultant force.
Always use the resultant force. Example: thrust 5000 N forwards and drag 1400 N backwards give F = 3600 N.
Required practical: force, mass and acceleration
diagram
A trolley on a bench is pulled by a string that passes over a pulley to a hanging mass. The weight of the hanging mass is the accelerating force.
Measure the acceleration with light gates and a data logger, or by timing the trolley over marked distances.
The weight of the hanging masses accelerates the trolley; the light gates measure the acceleration.
To vary the force at constant mass: move masses from the trolley to the hanger, so the total mass being accelerated stays the same.
To vary the mass at constant force: add masses to the trolley and keep the hanging mass the same.
Results: acceleration is proportional to force; acceleration decreases as mass increases.
How to answer each type of question
Calculate with F = m a
2 marksGrade 4
Check the mass is in kg.
Write F = m a, or its rearranged form, and substitute.
Give the unit.
Example. A resultant force of 450 N acts on a motorbike and rider. Their total mass is 300 kg. Calculate their acceleration.
Show the model answerHide the model answer
a = 450 ÷ 300 (1) a = 1.5 m/s2 (1)
Don’t lose marks
Using one of the forces instead of the resultant force.
Using a weight in N as if it were a mass in kg. If a weight is given, use m = W ÷ g.
Using a mass in grams: convert to kg first.
In the practical, adding new masses to the hanger, which changes the total mass as well as the force.
Saying acceleration is proportional to mass. It is inversely proportional.
More tips
Memory tricks
Formula triangle: F on top, m and a underneath.
Direction check: the acceleration always points the same way as the resultant force.
In the practical, moving masses from the trolley to the hanger changes the force without changing the total mass, so it is a fair test.
Rough values for estimates: car ~1000 kg, person ~70 kg.
Exam technique
F = m a must be recalled.
In estimates, state the values you assumed (e.g. 'mass of car ≈ 1000 kg') and use ~ or 'about' in your answer.
In practical questions, name the independent, dependent and control variables clearly.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 4
Calculate force using F = m aFor example, 1200 kg × 2.5 m/s2 = 3000 N.
Grade 5
Find mass or acceleration using F = maa = F ÷ m and m = F ÷ a.
Grade 5
Describe how acceleration depends on force and massAcceleration is proportional to the resultant force and inversely proportional to the mass.
Required practical:Acceleration (method, variables and exam tips)
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
Write down the equation that links acceleration (a), mass (m) and resultant force (F).
F = m a
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
(a) A car of mass 1200 kg accelerates at 2.5 m/s2. Calculate the resultant force on the car. Use the equation: resultant force = mass × acceleration[2]
(b) The same resultant force acts on a van with a greater mass than the car. How does the acceleration of the van compare with the acceleration of the car? Tick (✓) one box.[1]
It is smaller
It is the same
It is greater
(c) Complete the sentence. The acceleration of an object is ............ to the resultant force acting on the object. Tick (✓) one box.[1]
directly proportional
inversely proportional
equal
unrelated
Show the answer and mark scheme
(a)Answer: 3000 N
F = 1200 × 2.5
3000 (N)
(b)Answer: It is smaller
(c)Answer: directly proportional
Question 2Medium7 marks
(a) Write down the equation that links acceleration (a), mass (m) and resultant force (F).[1]
(b) A sprinter of mass 64 kg accelerates from rest to 8.0 m/s in 2.0 s. Calculate the average resultant force on the sprinter.[4]
(c) A second sprinter of the same mass experiences an average resultant force of 320 N. Calculate the average acceleration of the second sprinter.[2]