Newton’s Second Law (OCR Gateway GCSE Physics: Combined Science)

Revision Note

Katie M

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Katie M

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Newton's Second Law

  • Newton's second law of motion states:

The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to the object's mass

  • Newton's second law explains the following important principles:
    • An object will accelerate (change its velocity) in response to a resultant force
    • The bigger this resultant force, the larger the acceleration
    • For a given force, the greater the object's mass, the smaller the acceleration experienced

  • The image below shows some examples of Newton's second law in action:

Newton second law in action, downloadable IGCSE & GCSE Physics revision notes

Objects like baseballs and lawnmowers accelerate when a resultant force is applied on them. The size of the acceleration is proportional to the size of the resultant force

Calculating Force & Acceleration

  • Newton's second law can be expressed as an equation:

F = ma

  • Where:
    • F = resultant force on the object in Newtons (N)
    • m = mass of the object in kilograms (kg)
    • a = acceleration of the object in metres per second squared (m/s2)

  • This equation can be rearranged with the help of a formula triangle:

Fma Formula Triangle, downloadable IGCSE & GCSE Physics revision notes

Force, mass, acceleration formula triangle

Worked example

A car salesman says that his best car has a mass of 900 kg and can accelerate from 0 to 27 m/s in 3 seconds.Calculate:

a) The acceleration of the car in the first 3 seconds.

b) The force required to produce this acceleration.

Part (a)

Step 1: List the known quantities

    • Initial velocity = 0 m/s
    • Final velocity = 27 m/s
    • Time, t = 3 s

Step 2: Calculate the change in velocity

change in velocity = Δv = final velocity − initial velocity

Δv = 27 − 0 = 27 m/s

Step 3: State the equation for acceleration

a equals fraction numerator straight capital delta v over denominator t end fraction

Step 4: Calculate the acceleration

a = 27 ÷ 3 = 9 m/s2

Part (b)

Step 1: List the known quantities

    • Mass of the car, m = 900 kg
    • Acceleration, a = 9 m/s2

Step 2: Identify which law of motion to apply

    • The question involves quantities of force, mass and acceleration, so Newton's second law is required:

F = ma

Step 3: Calculate the force required to accelerate the car

F = 900 × 9 = 8100 N

Worked example

Three shopping trolleys, A, B and C, are being pushed using the same force. This force causes each trolley to accelerate.

WE Newton second law, downloadable IGCSE & GCSE Physics revision notes

Which trolley will have the smallest acceleration? Explain your answer.

Step 1: Identify which law of motion to apply

    • The question involves quantities of force and acceleration, and the image shows trolleys of different masses, so Newton's second law is required:

F = ma

Step 2: Re-arrange the equation to make acceleration the subject

a equals F over m

Step 3: Explain the inverse proportionality between acceleration and mass  

    • Acceleration is inversely proportional to mass
    • This means for the same amount of force, a large mass will experience a small acceleration
    • Therefore, trolley C will have the smallest acceleration because it has the largest mass

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.