Lesson focus: A resultant forceThe overall force on an object when all the forces acting on it are added together. changes velocity; balanced forces produce zero accelerationThe rate of change of velocity: acceleration = change in velocity ÷ time taken, measured in m/s²., not necessarily zero speed.
Draw collinear force diagrams, calculate resultant force and apply Newton’s first and second laws.
Build on earlier learning
Balanced and unbalanced forcesYear 7 introduced balanced and unbalanced forces. This lesson makes the resultant quantitative and links it to acceleration.
You will be successful when you can…
- Calculate a collinear resultant.
- Apply F = ma.
- Explain Newton’s first law.
- Distinguish force pairs from balanced forces.
Words that carry the science
- resultant force
- The single force with the same overall effect as all forces combined.
- inertia
- The tendency of an object to resist changes in velocity.
- equilibrium
- A state with zero resultant force and therefore zero acceleration.
- acceleration
- Rate of change of velocity.
- Newton’s first law
- An object remains at rest or at constant velocity unless acted on by a resultant force.
- Newton’s second law
- The resultant force equals mass multiplied by acceleration: F = ma.
Forces combine to one resultant
01Forces combine to one resultant
Choose one direction as positive and add forces with signs. A non-zero resultant forceThe overall force on an object when all the forces acting on it are added together. causes accelerationThe rate of change of velocity: acceleration = change in velocity ÷ time taken, measured in m/s². in the resultant’s direction.
Force arrows should start on the object, point in the force direction and use length to represent size when drawn to scale.
02Zero resultant means constant velocity
Newton's first lawAn object stays still or keeps moving at the same speed in a straight line unless an unbalanced force acts on it. states that zero resultant forceThe overall force on an object when all the forces acting on it are added together. gives zero acceleration. An object at rest stays at rest; a moving object continues at constant velocity.
Balanced forces can act on a moving car: driving force equals resistive force, so speed and direction stay constant.
03F = ma connects cause and response
For constant mass, F = ma means a larger resultant produces a larger acceleration. For the same resultant, a larger mass produces a smaller acceleration.
Newton’s third-law force pairs act on different objects, so they do not cancel on one free-body diagram. Balanced forces considered here act on the same object.
Balanced and unbalanced forces
A car's speed only changes when the forces on it are unbalanced. When the driving force equals the resistive forces, the car keeps a steady speed — or stays still.
Controls
Forces are illustrative (car mass 1000 kg). In space there is no air or road, so with the engine off the car keeps going at a steady speed: Newton’s first law.
Calculate acceleration
A 1200 kg car has 3600 N driving force and 1200 N resistive force.
- Choose forward as positive.
- Resultant force = 3600 − 1200 = 2400 N forward.
- Use a = F ÷ m = 2400 ÷ 1200.
- Acceleration = 2.0 m s⁻² forward.
How to make the reasoning visible: Only the resultant force belongs in F = ma, not the driving force alone.
Interpret force scenarios
Find the resultant and predict the motion change.
| Forward / N | Backward / N | Resultant / N | Motion consequence |
|---|---|---|---|
| 500 | 500 | 0 | constant velocity |
| 700 | 400 | 300 forward | accelerates forward |
| 300 | 650 | 350 backward | accelerates backward |
| 0 | 0 | 0 | rest or constant velocity |
Why can the first object still be moving?
Why do an action and reaction not cancel?
Check your understanding
Answer from memory, then check against the suggested answer.
State Newton’s first law.
What is the equation linking force, mass and acceleration?
What unit measures force?
A cyclist moves straight at constant speed. Compare driving and resistive forces.
Why does a passenger lurch forward when a car brakes?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
The same resultant force acts on an empty trolley and a loaded trolley. The loaded trolley accelerates less.
State the equation linking force, mass and acceleration, and rearrange it for acceleration.
(2)Explain why the loaded trolley accelerates less.
(3)Total for this question: 5 marks
Command word: For explainA command word: say how or why something happens, giving reasons with words like "because" or "so"., name the controlled quantity and use the rearranged relationship to show the causal comparison.