Newton's Second Law: acceleration, a, in metres per second squared, m/s²

The idea

Acceleration is the rate of change of velocity and is measured in metres per second squared, m/s². An acceleration of 3 m/s² means the velocity increases by 3 m/s every second. In Newton's Second Law, F = m × a, acceleration must be in m/s² so that a mass in kilograms gives a force in newtons. Acceleration is a vector: speeding up, slowing down and changing direction all involve acceleration. Calculate it using a = Δv ÷ t, where Δv is the change in velocity in m/s and t is the time in s. For example, a runner reaching 8 m/s from rest in 4 s has a = 8 ÷ 4 = 2 m/s². Rearranged, a = F ÷ m, so the same force produces greater acceleration on a smaller mass.

What earns the marks

• State that acceleration is measured in metres per second squared (m/s²) and is the rate of change of velocity.
• Calculate acceleration using a = Δv ÷ t, ensuring velocity change is in m/s and time is in s.
• Use a = F ÷ m to find acceleration from force in newtons and mass in kilograms.
• Interpret an acceleration such as 5 m/s² as a velocity increase of 5 m/s each second.
• Recognise acceleration as a vector quantity, so deceleration and direction change are also accelerations.

Common mistakes and how to put them right

• Writing the unit as m/s, which is a velocity unit.

  Put it right by writing m/s² for acceleration.

• Dividing final velocity by time without subtracting the initial velocity.

  Put it right by using the change in velocity, Δv.

• Mixing units, such as using time in minutes with velocity in m/s.

  Put it right by converting time to seconds first.

Exam tips

• Show the change in velocity calculation separately before dividing by time.
• Include the direction when an acceleration is negative or opposes motion, describing it as deceleration.
• Check that the unit of your answer matches m/s², since a unit of m/s indicates velocity was calculated instead.