Newton's First and Second Laws

This lesson covers Newton's first law and Newton's second law of motion as required by AQA GCSE Combined Science Trilogy (8464), section 6.5.3. These laws link forces to the motion of objects and form the backbone of the Forces topic.

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Newton's First Law

Newton's first law: An object at rest remains at rest, and an object in motion continues to move at a constant velocity, unless acted upon by a resultant (net) force.

In plain language:

• If the resultant force on an object is zero, the object either stays still or keeps moving at the same speed in the same direction.
• If the resultant force is not zero, the object will accelerate (change its velocity).

What Is Inertia?

Inertia is the tendency of an object to resist a change in its state of motion. The more massive an object, the greater its inertia and the harder it is to change its motion.

• A stationary object with high inertia (large mass) requires a large force to start it moving.
• A moving object with high inertia requires a large force to stop it or change its direction.

Exam Tip (AQA 8464): Newton's first law is really about inertia. When a car brakes suddenly, passengers continue moving forward — this is because of their inertia. Seatbelts provide the resultant force needed to decelerate the passenger.

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Newton's First Law — Examples

Situation	Resultant force	What happens
Book on a table	Zero (weight = normal force)	Stays stationary
Car at constant speed	Zero (driving force = resistive forces)	Continues at constant velocity
Ball kicked across grass	Non-zero (friction acts backwards)	Decelerates and stops
Satellite in deep space (no friction)	Zero	Moves at constant velocity forever

flowchart TD
    RF["Resultant Force"]
    RF -->|"= 0"| ZF["Object at rest → stays at rest\nObject moving → constant velocity"]
    RF -->|"≠ 0"| NZ["Object ACCELERATES in the direction of the resultant force"]

    style RF fill:#f39c12,color:#fff
    style ZF fill:#27ae60,color:#fff
    style NZ fill:#e74c3c,color:#fff

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Newton's Second Law

Newton's second law: The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.

$F = m \times a$F=m×a

Where:

• F = resultant force (N)
• m = mass (kg)
• a = acceleration (m/s²)

Understanding the Equation

• If you double the force (keeping mass constant), the acceleration doubles.
• If you double the mass (keeping force constant), the acceleration halves.
• The direction of the acceleration is the same as the direction of the resultant force.

Rearranging $F = ma$F=ma

To find	Equation
Force	$F = m \times a$F=m×a
Mass	$m = F / a$m=F/a
Acceleration	$a = F / m$a=F/m

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Worked Examples

Example 1 — Calculating Force

A trolley of mass 2 kg accelerates at 3 m/s². Calculate the resultant force.

Solution:

$F = m \times a = 2 \times 3 = 6$F=m×a=2×3=6 N

Example 2 — Calculating Acceleration

A resultant force of 500 N acts on a car of mass 1000 kg. Calculate the acceleration.

Solution:

$a = \frac{F}{m} = \frac{500}{1000} = 0.5$a=mF​=1000500​=0.5 m/s²

Example 3 — Calculating Mass

A force of 120 N causes an acceleration of 4 m/s². Calculate the mass of the object.

Solution:

$m = \frac{F}{a} = \frac{120}{4} = 30$m=aF​=4120​=30 kg

Example 4 — Finding the Resultant Force First

A 1500 kg car has a driving force of 4000 N and resistive forces totalling 1000 N. Calculate the acceleration.

Solution:

Step 1: Find the resultant force. $F_{\text{resultant}} = 4000 - 1000 = 3000$Fresultant​=4000−1000=3000 N forwards

Step 2: Calculate acceleration. $a = \frac{F}{m} = \frac{3000}{1500} = 2$a=mF​=15003000​=2 m/s²

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Linking Newton's First and Second Laws

Newton's first law is actually a special case of the second law. When $F = 0$F=0:

$0 = m \times a$0=m×a → $a = 0$a=0 → no change in velocity

This means the object stays at rest or continues at constant velocity — which is exactly what Newton's first law states.

flowchart LR
    F["F = ma"] -->|"F = 0"| N1["a = 0 → Newton’s First Law\n(constant velocity or at rest)"]
    F -->|"F ≠ 0"| N2["a ≠ 0 → Newton’s Second Law\n(object accelerates)"]

    style F fill:#8e44ad,color:#fff
    style N1 fill:#27ae60,color:#fff
    style N2 fill:#e74c3c,color:#fff

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Applying Newton's Second Law to Falling Objects

When an object falls under gravity (ignoring air resistance):

$F = W = m \times g$F=W=m×g

$m \times a = m \times g$m×a=m×g

$a = g = 9.8$a=g=9.8 m/s²

All objects fall with the same acceleration ($g$g) when air resistance is negligible, regardless of their mass. This is why a feather and a hammer fall at the same rate in a vacuum.

When air resistance is present, the resultant force is:

$F_{\text{resultant}} = W - \text{air resistance}$Fresultant​=W−air resistance

So the acceleration is less than $g$g and decreases as speed increases, until terminal velocity is reached ($a = 0$a=0).

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Estimating Forces — Everyday Situations

AQA may ask you to estimate the force involved in everyday situations. Use $F = ma$F=ma with reasonable estimates.

Situation	Estimated mass	Estimated acceleration	Estimated force
Pushing a shopping trolley	30 kg	0.5 m/s²	15 N
Kicking a football	0.4 kg	50 m/s²	20 N
Braking a car	1200 kg	5 m/s²	6000 N

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Common Mistakes

• Thinking that a resultant force is needed to keep an object moving — it is only needed to change the velocity.
• Using total force instead of resultant force in $F = ma$F=ma — always calculate the resultant first.
• Forgetting that $F$F in $F = ma$F=ma is the resultant force, not just any single force.
• Confusing mass and weight — $F = ma$F=ma uses mass (kg), not weight (N).
• Not including units in the final answer.

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Summary