Pearson Edexcel · A-Level · Mathematics
Course version: 9MA0 · Version from Mar 2026
Understand and use Newton’s second law for motion in a straight line…
Full specification wording
Forces and Newton’s laws: 8.2 Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors); extend to situations where forces need to be resolved (restricted to 2 dimensions).
Newton’s second law states that the resultant force on a particle equals mass times acceleration: F = ma.
Checked against the Pearson Edexcel 9MA0 specification (opens in a new tab) on .
- Point 2 of 6
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Newton’s second law states that the resultant force on a particle equals mass times acceleration: F = ma. For motion in a straight line, resolve all forces along the direction of motion and perpendicular to it. If forces are given as 2-D vectors, add them component-wise to find the resultant, then apply F = ma to each component. When forces act at angles, resolve each into two perpendicular directions using F cos θ and F sin θ, choosing axes along and perpendicular to the motion. For example, a 5 kg block on a smooth horizontal surface pulled by a 20 N force at 30° above the horizontal: horizontal component = 20 cos 30° ≈ 17.32 N, so a = 17.32 ÷ 5 ≈ 3.46 m s⁻². Perpendicular to motion, forces balance if there is no vertical acceleration. Always state the direction of positive motion and check units: force in N, mass in kg, acceleration in m s⁻².
What earns the marks
- State Newton’s second law as F = ma, where F is the resultant force in newtons, m is mass in kilograms and a is acceleration in m s⁻².
- Resolve forces into two perpendicular directions, typically along the line of motion and perpendicular to it, using trigonometry.
- For 2-D vector forces, add components in each direction separately to obtain the resultant force vector.
- Apply F = ma independently in each perpendicular direction, setting the perpendicular resultant to zero when there is no acceleration in that direction.
- Use consistent sign conventions for forces acting in opposite directions along the line of motion.
Common mistakes and how to put them right
Adding force magnitudes directly without resolving when forces act at angles.
Put it right by resolving each force into perpendicular components before summing.
Forgetting to include weight or normal reaction in the perpendicular direction.
Put it right by drawing a complete force diagram showing all forces.
Using the total force instead of the resultant force in F = ma.
Put it right by subtracting opposing forces to find the resultant first.
Exam tips
- Draw a clear force diagram with all forces labelled and axes chosen before writing equations.
- Show the resolution step explicitly, writing component expressions such as F cos θ and F sin θ with the angle identified.
- Check that the final acceleration has the correct magnitude and direction, and include units in your answer.
Try the lesson
The start of the Forces and Newton’s laws: 8.2 Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors); extend to situations where forces need to be resolved (restricted to 2 dimensions). lesson, made from checked teaching notes for this specification point.
Have a go first
A particle of mass 4 kg is pulled along a smooth horizontal surface by a horizontal force of 12 N. Using Newton's second law, find the acceleration of the particle.
Listen
Newton’s second law states that the resultant force on a particle equals mass times acceleration: F = ma. For motion in a straight line, resolve all forces along the direction of motion and perpendicular to it. If forces are given as 2-D vectors, add them component-wise to find the resultant, then apply F = ma to each component. When forces act at angles, resolve each into two perpendicular directions using F cos θ and F sin θ, choosing axes along and perpendicular to the motion. For example, a 5 kg block on a smooth horizontal surface pulled by a 20 N force at 30° above the horizontal: horizontal component = 20 cos 30° ≈ 17.32 N, so a = 17.32 ÷ 5 ≈ 3.46 m s⁻². Perpendicular to motion, forces balance if there is no vertical acceleration. Always state the direction of positive motion and check units: force in N, mass in kg, acceleration in m s⁻². A strong answer earns marks for these points. State Newton’s second law as F = ma, where F is the resultant force in newtons, m is mass in kilograms and a is acceleration in m s⁻². Resolve forces into two perpendicular directions, typically along the line of motion and perpendicular to it, using trigonometry. For 2-D vector forces, add components in each direction separately to obtain the resultant force vector. Apply F = ma independently in each perpendicular direction, setting the perpendicular resultant to zero when there is no acceleration in that direction. A common slip: Adding force magnitudes directly without resolving when forces act at angles. Instead, resolving each force into perpendicular components before summing. Exam tip: Draw a clear force diagram with all forces labelled and axes chosen before writing equations.
See it
Put it in order
Put these steps in the order they happen.
- 1. Check magnitude, direction and units: N, kg, m s⁻²
- 2. Perpendicular direction: set resultant to zero when there is no acceleration
- 3. Resolve each force into two perpendicular directions using F cos θ and F sin θ
- 4. Apply F = ma in the direction of motion
- 5. Draw a clear force diagram with all forces labelled and axes chosen
- 6. State the direction of positive motion
- 7. Add components in each direction separately to obtain the resultant force
Key words
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Newton’s second law
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Resultant force
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Resolution of forces
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See every definition
- Newton’s second law
- The resultant force on a particle equals mass times acceleration, written F = ma.
- Resultant force
- The single force found by adding forces component-wise, or by subtracting opposing forces, before applying F = ma.
- Resolution of forces
- Splitting each force acting at an angle into two perpendicular directions using F cos θ and F sin θ.
Label the diagram
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1Box 1
2Box 2
3Box 3
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Test your understanding of Forces and Newton’s laws: 8.2 Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2-D vectors); extend to situations where forces need to be resolved (restricted to 2 dimensions).
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