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 Video by Zeeshan Zamurred Forces and Motion

Edexcel AS Level Maths: 10.3 Forces and AccelerationWatch the full walkthrough 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

Newton's second law

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

F = ma

F

is the RESULTANT force, in newtons.

a = \frac{F}{m} = \frac{12}{3}

Answer

4

m/s²

Using the resultant

The $F$ in $F = ma$ is always the $resultant$ (net) force, so first combine all the forces. Often you resolve forces and apply $F = ma$ in one direction (e.g. horizontally) and equilibrium ( $Σ F = 0$ ) 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.

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 $ma$ to solve for the unknown.

1Resultant

= 30 - 10 = 20

a = \frac{20}{5}

Answer

4

m/s²

Formula recap

F = ma

Newton's second law (F = resultant).

a = \frac{F _{resultant}}{m}

Acceleration from net force.

F_{res} = driving - 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).

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