Newton’s Second Law | HL IB Physics Revision Notes 2025

Newton's Second Law

Newton's second law of motion states:

The resultant force on an object is directly proportional to its acceleration

This can also be written as:

$F = m a$

Where:
- F = resultant force (N)
- m = mass (kg)
- a = acceleration (m s^–2)
This relationship means that objects will accelerate if there is a resultant force acting upon then

An unbalanced force acting on a body means it experiences a resultant force
- If the resultant force is along the direction of motion, it will speed up (accelerate) or slow down (decelerate) the body
- If the resultant force is at an angle, it will change the direction of the body

Worked example

A girl is riding her skateboard down the road and increases her speed from 1 m s^–1 to 4 m s^–¹ in 2.5 s. The force driving her forward is 72 N. Calculate the combined mass of the girl and the skateboard. WE - Newtons second law question image, downloadable AS & A Level Physics revision notes

WE - Newtons second law answer image, downloadable AS & A Level Physics revision notes

Resultant Force

Since force is a vector, every force on a body has a magnitude and direction
- The resultant force is, therefore, the vector sum of all the forces acting on the body
The direction is given by either the positive or negative direction as shown in the examples below

Resultant Force horizontal, downloadable AS & A Level Physics revision notes

Resultant forces on a body can be positive or negative depending on their direction

The resultant force could also be at an angle, in which case, the magnitude and direction of the resultant force can be determined using either:
- Calculation (usually simple geometry, such as Pythagoras' Theorem or the sine and cosine rules)
- Scale drawing
This is covered further in Scale Diagrams

Acceleration

Since acceleration is a vector, it can be either positive or negative depending on the direction of the resultant force
- If the resultant force is in the same direction as the motion of an object, the acceleration is positive
- If the resultant force is in the opposite direction to the motion of an object, the acceleration is negative

An object may continue in the same direction however with a resultant force in the opposite direction to its motion
- This means it will slow down (decelerate) and eventually come to a stop

1-2-3-resultant-force-acceleration-ib-2025-physics

If there are no drag forces, or they're negligible, the acceleration is independent of the mass of an object
- This has been shown in experiments by astronauts who have dropped a feather and a hammer on the Moon from the same height
- Both the hammer and feather drop to the Moon's surface at the same time

Worked example

Three forces, 4 N, 8 N, and 24 N act on an object with a mass of 5 kg. Which acceleration is not possible with any combination of these three forces?

A. 1 m s^–²

B. 4 m s^–²

C. 7 m s^–²

D. 10 m s^–^²

Answer:

Step 1: List the values given

Three possible forces at any angle of choice: 4 N, 8 N, and 24 N
Mass of object = 5 kg

Step 2: Consider the relevant equation

Newton's second law relates force and acceleration:

F = m × a

Step 3: Rearrange to make acceleration the focus

$a = \frac{F}{m}$

Step 4: Investigate the minimum possible acceleration

The minimum acceleration would occur when the forces were acting against each other
This is when just the 4 N force is acting on the body
Now check the acceleration:

$\frac{4}{5} = 0.8 m s^{- 2}$

Step 4: Investigate the maximum possible acceleration

The maximum acceleration would occur when all three forces are acting in the same direction
This is a total force of

4 + 8 + 24 = 36 N

With acceleration:

$\frac{36}{5} = 7.2 m s^{- 2}$

Step 5: Consider this range and the options

Since option D is higher than 7.2 m s^–²; it is not possible that these three forces can produce 10 m s^–²acceleration for this mass
Option D is the correct answer, as it is the only one that is not possible

Worked example

A rocket produces an upward thrust of 15 MN and has a weight of 8 MN.

(a)

When in flight, the force due to air resistance is 500 kN. Determine the resultant force on the rocket.

(b)

The mass of the rocket is 0.8 × 10⁵ kg.

Calculate the magnitude and direction of the acceleration of the rocket.

WE - Newtons second law on rocket answer image(1), downloadable AS & A Level Physics revision notes

Exam Tip

The direction you consider positive is your choice, as long as the signs of the numbers (positive or negative) are consistent throughout the question.

It is a general rule to consider the direction the object is initially travelling in as positive. Therefore all vectors in the direction of motion will be positive and opposing vectors, such as drag forces, will be negative.

Newton’s Second Law (HL IB Physics)

Revision Note