AQA · GCSE · Physics

    Course version: 8463 · Version from Sept 2016

    Newton's Second Law: F = m a

    Newton's second law links the resultant force on an object to its mass and acceleration through F = m a.

    Checked against the AQA 8463 specification (opens in a new tab) on .

    • Point 3 of 11
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    Newton's second law links the resultant force on an object to its mass and acceleration through F = m a. Here F is the resultant force in newtons, m is the mass in kilograms and a is the acceleration in metres per second squared. The equation shows that a larger resultant force produces a larger acceleration for the same mass, while a larger mass needs a larger force for the same acceleration. For example, a 1200 kg car with a resultant forward force of 3600 N accelerates at 3600 ÷ 1200 = 3 m s⁻². Rearranged, a = F ÷ m and m = F ÷ a. Always use the resultant force, found by adding or subtracting all forces along the line of motion, and keep units consistent before substituting.

    What earns the marks

    • State the equation as F = m a and identify F as the resultant force in newtons, m as mass in kilograms and a as acceleration in metres per second squared.
    • Substitute values into F = m a with consistent SI units, converting grams to kilograms and kilometres per hour to metres per second where needed.
    • Rearrange the equation correctly to find acceleration using a = F ÷ m or mass using m = F ÷ a.
    • Calculate the resultant force by combining all forces acting along the line of motion before using F = m a.
    • Interpret a numerical answer in context, for example stating that doubling the resultant force doubles the acceleration when mass is unchanged.

    Common mistakes and how to put them right

    • Using one individual force instead of the resultant force.

      Put it right by adding forces in the same direction and subtracting forces in the opposite direction first.

    • Substituting mass in grams or force in kilonewtons without converting.

      Put it right by converting to kilograms and newtons before calculating.

    • Rearranging incorrectly, such as dividing mass by force when finding acceleration.

      Put it right by using a = F ÷ m and checking the rearrangement by substituting simple numbers.

    Exam tips

    • Write the equation, then the substituted values with units, then the answer with its unit; this makes method clear even if the final arithmetic slips.
    • Underline the word resultant in a question and show the addition or subtraction of forces before using F = m a.
    • Check the size and unit of your answer: a car accelerating at 3 m s⁻² is reasonable, while 3000 m s⁻² suggests a unit or rearrangement error.

    Try the lesson

    The start of the Newton's Second Law: F = m a lesson, made from checked teaching notes for this specification point.

    Have a go first

    A trolley of mass 4 kg accelerates at 3 m/s². Using F = m a, what is the resultant force on the trolley?

    Listen

    Newton's second law links the resultant force on an object to its mass and acceleration through F = m a. Here F is the resultant force in newtons, m is the mass in kilograms and a is the acceleration in metres per second squared. The equation shows that a larger resultant force produces a larger acceleration for the same mass, while a larger mass needs a larger force for the same acceleration. For example, a 1200 kg car with a resultant forward force of 3600 N accelerates at 3600 ÷ 1200 = 3 m s⁻². Rearranged, a = F ÷ m and m = F ÷ a. Always use the resultant force, found by adding or subtracting all forces along the line of motion, and keep units consistent before substituting. A strong answer earns marks for these points. State the equation as F = m a and identify F as the resultant force in newtons, m as mass in kilograms and a as acceleration in metres per second squared. Substitute values into F = m a with consistent SI units, converting grams to kilograms and kilometres per hour to metres per second where needed. Rearrange the equation correctly to find acceleration using a = F ÷ m or mass using m = F ÷ a. Calculate the resultant force by combining all forces acting along the line of motion before using F = m a. A common slip: Using one individual force instead of the resultant force. Instead, adding forces in the same direction and subtracting forces in the opposite direction first. Exam tip: Write the equation, then the substituted values with units, then the answer with its unit; this makes method clear even if the final arithmetic slips.

    See it

    A top-to-bottom flowchart with six steps. The first step is to find the resultant force by adding forces in the same direction and subtracting forces in the opposite direction. An arrow leads to the second step, converting to consistent SI units with mass in kilograms and force in newtons. An arrow leads to the third step, choosing the rearrangement: F = m a, a = F ÷ m, or m = F ÷ a. An arrow leads to the fourth step, substituting the values with units. An arrow leads to the fifth step, calculating the answer with its unit. A final arrow leads to the sixth step, interpreting the answer in context.
    The sequence of steps for using F = m a, from finding the resultant force and converting units through to calculating and interpreting the answer.

    Put it in order

    Put these steps in the order they happen.

    1. 1. Choose the rearrangement: F = m a, a = F ÷ m, or m = F ÷ a
    2. 2. Convert to consistent SI units: mass in kilograms, force in newtons
    3. 3. Find the resultant force: add forces in the same direction, subtract forces in the opposite direction
    4. 4. Interpret the answer in context
    5. 5. Calculate the answer with its unit
    6. 6. Substitute the values with units

    Key words

    Say what each word means before you turn the card.

    Resultant force

    Try answering aloud or in your head before turning the card.

    F = m a

    Try answering aloud or in your head before turning the card.

    Rearranging equations

    Try answering aloud or in your head before turning the card.

    SI units and unit conversion

    Try answering aloud or in your head before turning the card.

    See every definition
    Resultant force
    Found by adding or subtracting all forces along the line of motion, and it must always be used in F = m a.
    F = m a
    Equation linking the resultant force in newtons, the mass in kilograms and the acceleration in metres per second squared.
    Rearranging equations
    The equation can be rearranged to a = F ÷ m to find acceleration or m = F ÷ a to find mass.
    SI units and unit conversion
    Keep units consistent before substituting, converting grams to kilograms and kilometres per hour to metres per second where needed.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-to-bottom flowchart with six steps. The first step is to find the resultant force by adding forces in the same direction and subtracting forces in the opposite direction. An arrow leads to the second step, converting to consistent SI units with mass in kilograms and force in newtons. An arrow leads to the third step, choosing the rearrangement: F = m a, a = F ÷ m, or m = F ÷ a. An arrow leads to the fourth step, substituting the values with units. An arrow leads to the fifth step, calculating the answer with its unit. A final arrow leads to the sixth step, interpreting the answer in context.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

    There is more to this lesson

    The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.

    Carry on with the full lesson

    A week of Premium from your first lesson · Then the free plan continues · No card, no charge

    Test your understanding of Newton's Second Law: F = m a

    Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.

    Take topic quiz

    A week of Premium from your first lesson · Then the free plan continues · No card, no charge

    Start free

    Cookies on MasteryMind

    Essential cookies keep you signed in.

    Analytics and advertising cookies stay off unless you accept.

    Read our Privacy Policy.