Newton's Second Law: F = m a

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 2 kg trolley pushed with a resultant force of 6 N accelerates at 3 m/s² because 6 ÷ 2 = 3. 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 that F is the resultant force in newtons, m is the mass in kilograms and a is the acceleration in metres per second squared.
• Use the equation in the form F = m a, or rearrange it to a = F ÷ m or m = F ÷ a, as the question requires.
• Calculate the resultant force by combining all forces acting along the line of motion before substituting into the equation.
• Substitute values with consistent units, for example convert grams to kilograms and show the arithmetic clearly.
• Interpret a numerical answer in context, such as stating the direction of the acceleration or explaining what a larger mass does to the acceleration for a fixed force.

Common mistakes and how to put them right

• Using a single applied force instead of the resultant force.

  Put it right: Add or subtract all forces along the line of motion first, then substitute.

• Mixing units, such as using grams with newtons.

  Put it right: Convert mass to kilograms before calculating.

• Rearranging incorrectly, for example writing a = m ÷ F.

  Put it right: Check by substituting simple numbers, since a larger mass must give a smaller acceleration for the same force.

Exam tips

• Write the equation, then the rearranged form, then substitute values, so the examiner can follow your method.
• Check the unit of every value before calculating and convert grams to kilograms or centimetres to metres where needed.
• Give the unit with your final answer and add a short sentence explaining what the result means in the context of the question.