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M10.3MechanicsStretch

Forces and Acceleration

Newton’s second law, F = ma, is the heart of mechanics: the resultant force on an object equals its mass times its acceleration. It links the forces in a diagram to how the object actually moves.

30 min Forces and Motion
Edexcel AS Level Maths: 10.3 Forces and AccelerationCurated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • State Newton’s second law
  • Apply F = ma to find force or acceleration
  • Use the resultant force in the direction of motion
  • Combine F = ma with force diagrams
1

Newton's second law

The resultant\textbf{resultant} force equals mass times acceleration. Force and acceleration are vectors in the same direction, so you usually apply F=maF = ma along the direction of motion.

F=maF = ma
FF is the RESULTANT force, in newtons.
Example 1A resultant force of 12 N acts on a 3 kg mass. Find the acceleration.
1a=Fm=123a = \dfrac{F}{m} = \dfrac{12}{3}.
Answer44 m/s²
2

Using the resultant

The FF in F=maF = ma is always the resultant\textbf{resultant} (net) force, so first combine all the forces. Often you resolve forces and apply F=maF = ma in one direction (e.g. horizontally) and equilibrium (ΣF=0\Sigma F = 0) in the perpendicular one.

Tip — Find the resultant force FIRST, then divide by mass — F in F = ma is the net force, not a single force.

3

With a force diagram

The standard method: draw the force diagram, find the resultant in the direction of motion (e.g. driving force minus friction), then set it equal to mama to solve for the unknown.

Example 1A 5 kg box is pulled by 30 N against 10 N friction. Find its acceleration.
1Resultant =30−10=20= 30 - 10 = 20 N.
2a=205a = \dfrac{20}{5}.
Answer44 m/s²

Formula recap

F=maF = ma
Newton's second law (F = resultant).
a=Fresultantma = \dfrac{F_{\text{resultant}}}{m}
Acceleration from net force.
Fres=driving−resistiveF_{\text{res}} = \text{driving} - \text{resistive}
Net force along motion.

Common mistakes to avoid

Using a single force as F instead of the resultant.
F in F = ma is the net (resultant) force — combine forces first.
Forgetting to subtract friction/resistance.
The resultant is driving force minus resistive forces.

Key takeaways

  • Newton’s second law: F = ma, with F the resultant force.
  • Combine forces to get the net force before applying F = ma.
  • Resolve along motion (F = ma) and perpendicular (equilibrium).

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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