Force, mass and acceleration GCSE physics questions are solved with Newton's second law: force (N) equals mass (kg) multiplied by acceleration (m/s²), written F = ma. Find the resultant force first, choose the correct rearrangement of the formula for whatever you need, then substitute values carefully with matching units.
What is Newton's second law of motion?
Newton's second law states that the acceleration of an object is directly proportional to the resultant force acting on it, and inversely proportional to its mass. It is written as:
F = m × a
Where:
- F = resultant force (newtons, N)
- m = mass (kilograms, kg)
- a = acceleration (metres per second squared, m/s²)
This means a bigger resultant force produces a bigger acceleration, and a bigger mass produces a smaller acceleration for the same force — a shopping trolley accelerates far faster than a loaded lorry under an identical push.
What is resultant force?
Before using F = ma, you usually need to find the resultant force — the single overall force acting on an object once all individual forces have been combined, taking direction into account.
- Forces acting in the same direction are added together.
- Forces acting in opposite directions are subtracted from each other.
Example: A box is pushed forward with 80 N while friction acts backward with 30 N. The resultant force = 80 − 30 = 50 N forward.
If the resultant force on an object is zero, the object's velocity does not change — it either stays still or continues at a constant velocity in a straight line.
How do you calculate force, mass and acceleration step by step?
Use this method for any F = ma question, whether you are finding force, mass, or acceleration:
- Identify the resultant force by adding or subtracting all the forces acting on the object.
- Write down the known quantities and identify which one you need to find.
- Rearrange F = ma to make the unknown quantity the subject.
- Substitute the known values, making sure units are in newtons, kilograms, and m/s².
- Calculate the answer and state it with the correct unit.
How do you rearrange F = ma?
Depending on what the question asks for, rearrange the formula as follows:
| To find | Rearranged formula |
|---|---|
| Force (N) | F = m × a |
| Acceleration (m/s²) | a = F ÷ m |
| Mass (kg) | m = F ÷ a |
Always sense-check your answer before moving on. A resultant force of a few thousand newtons is plausible for a family car; an answer a thousand times bigger or smaller usually means a units slip — most often grams left unconverted to kilograms.
Worked example 1: calculating force
A resultant force accelerates a 1,200 kg car at 2.5 m/s². What is the resultant force?
- F = m × a
- F = 1,200 × 2.5 = 3,000 N
Worked example 2: calculating acceleration
A resultant force of 20 N acts on a 5 kg trolley. What is its acceleration?
- a = F ÷ m
- a = 20 ÷ 5 = 4 m/s²
Worked example 3: calculating mass
A resultant force of 45 N gives an object an acceleration of 3 m/s². What is the object's mass?
- m = F ÷ a
- m = 45 ÷ 3 = 15 kg
Worked example 4: finding the resultant force first
A 10 kg sledge is pulled forward with a force of 60 N while friction acts backward with 15 N. What is the sledge's acceleration?
Step 1 — find the resultant force:
Resultant force = 60 − 15 = 45 N forward
Step 2 — apply a = F ÷ m:
- a = 45 ÷ 10 = 4.5 m/s²
This two-step approach — resultant force first, then F = ma — is the most common way GCSE exam questions combine force diagrams with calculations.
Frequently asked questions
What is the equation for force, mass and acceleration?
The equation is F = m × a, where F is the resultant force in newtons, m is mass in kilograms, and a is acceleration in metres per second squared. It can be rearranged to find acceleration (a = F ÷ m) or mass (m = F ÷ a), depending on which quantity the question asks for.
How do you find the resultant force before using F = ma?
Add together all forces acting in the same direction, then subtract any forces acting in the opposite direction. The single value left over is the resultant force. If the forces are balanced, the resultant force is zero and the object's velocity stays constant.
What units do you use in F = ma calculations?
Force must be in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). If a question gives mass in grams, convert it to kilograms first by dividing by 1,000, otherwise the calculated force will be 1,000 times too large.
Why does a heavier object accelerate more slowly under the same force?
Because acceleration is inversely proportional to mass in Newton's second law (a = F ÷ m), dividing the same force by a larger mass gives a smaller acceleration. This is why a fully loaded lorry accelerates far more slowly than an empty car under an identical engine force.
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