top of page

10.1 Force and Acceleration

GCSE Physics · AQA · Chapter 10: Force and Motion

A free GCSE Physics lesson for AQA (8463) from OBA School: newton’s first and second laws, using F = m a, and (Higher tier) inertia and inertial mass. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Use Newton’s first law to explain the motion of an object when the forces on it are balanced
  • Describe how the acceleration of an object depends on the resultant force on it and on its mass (Newton’s second law)
  • Calculate force, mass or acceleration using F = m a, rearranging the equation and converting units
  • Explain why an object speeds up or slows down depending on the direction of the resultant force
  • (Higher tier) explain what inertia means and calculate inertial mass as force ÷ acceleration

Key words

  • Resultant force: The single force that has the same effect as all the forces acting on an object together.
  • Newton’s first law: If the resultant force on an object is zero, it stays at rest or keeps moving at the same speed in the same direction.
  • Newton’s second law: The acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass.
  • Newton (N): The unit of force. 1 N gives a mass of 1 kg an acceleration of 1 m/s².
  • Directly proportional: Doubling one quantity doubles the other; the graph is a straight line through the origin. Symbol ∝.
  • Inversely proportional: Doubling one quantity halves the other.
  • Inertia: (Higher tier) The tendency of an object to stay at rest or to keep moving with a constant velocity.
  • Inertial mass: (Higher tier) A measure of how difficult it is to change the velocity of an object: force ÷ acceleration.

Resultant force and Newton’s first law

Most objects have several forces acting on them. To predict how an object moves, add the forces together, taking direction into account, to find the resultant force. Forces in the same direction add; forces in opposite directions subtract.

Newton’s first law: if the resultant force on an object is zero, the object’s velocity does not change.

  • A stationary object stays stationary.
  • A moving object keeps moving at the same speed in the same direction. A car cruising at a steady 25 m/s on a straight road has a driving force exactly balanced by the resistive forces.

Key fact: A resultant force is needed to change velocity (speed up, slow down or change direction), not to keep an object moving.

Newton’s second law: F = m a

Experiments with trolleys show two things about the acceleration of an object:

  • For a fixed mass, acceleration is directly proportional to the resultant force (a ∝ F). Double the force and the acceleration doubles.
  • For a fixed force, acceleration is inversely proportional to the mass (a ∝ 1/m). Double the mass and the acceleration halves.

resultant force = mass × acceleration F = m a

F = resultant force in newtons, N; m = mass in kilograms, kg; a = acceleration in metres per second squared, m/s²

Rearranged: a = F ÷ m and m = F ÷ a

So 1 N is the resultant force that gives a 1 kg mass an acceleration of 1 m/s².

Worked example: force on a go-kart

A go-kart and its driver have a total mass of 150 kg. They accelerate at 2.4 m/s². Calculate the resultant force.
F = m a = 150 kg × 2.4 m/s²

Answer: F = 360 N

Rearranging and converting units

Worked example: finding acceleration

A toy car of mass 250 g has a resultant force of 0.15 N on it. Calculate its acceleration.
Convert: 250 g = 250 ÷ 1000 = 0.250 kg
a = F ÷ m = 0.15 N ÷ 0.250 kg

Answer: a = 0.60 m/s²

Worked example: finding mass

A resultant force of 4.5 kN gives a van an acceleration of 1.8 m/s². Calculate the mass of the van.
Convert: 4.5 kN = 4500 N
m = F ÷ a = 4500 N ÷ 1.8 m/s²

Answer: m = 2500 kg

Exam tip: Always change grams to kilograms (÷ 1000) and kilonewtons to newtons (× 1000) before you substitute into F = m a.

Speeding up and slowing down

The acceleration of an object is always in the same direction as the resultant force.

  • Resultant force in the same direction as the velocity: the object speeds up (positive acceleration).
  • Resultant force in the opposite direction to the velocity: the object slows down. This is a deceleration (negative acceleration).

In a force and acceleration experiment, a computer can plot a velocity–time graph for the trolley. The gradient of the line is the acceleration.

Worked example: a cyclist braking

A cyclist and bike (total mass 75 kg) slow from 8.0 m/s to 2.0 m/s in 3.0 s. Calculate the resultant force.
a = (v − u) ÷ t = (2.0 − 8.0) ÷ 3.0 = −2.0 m/s²
F = m a = 75 × (−2.0) = −150 N (the minus sign means the force acts backwards)

Answer: 150 N opposite to the direction of motion

Inertia and inertial mass (Higher tier)

Every object tends to keep doing what it is already doing: staying at rest or moving at a constant velocity. This tendency is called inertia. A loaded lorry is much harder to start or stop than an empty one.

The inertial mass of an object measures how difficult it is to change its velocity. It is defined by:

inertial mass = force ÷ acceleration m = F ÷ a

Worked example: comparing inertial masses

The same 6.0 N resultant force acts on two pucks. Puck P accelerates at 3.0 m/s²; puck Q at 1.5 m/s².
P: m = 6.0 ÷ 3.0 = 2.0 kg Q: m = 6.0 ÷ 1.5 = 4.0 kg
Q has the larger inertial mass, so its velocity is harder to change.

Answer: 2.0 kg and 4.0 kg

Common mistakes

  • Putting just one of the forces into F = m a. Always find the resultant force first.
  • Forgetting to convert grams to kilograms or kN to N before calculating.
  • Thinking a moving object needs a resultant force to keep it moving. At constant velocity the resultant force is zero.
  • Writing the unit of acceleration as m/s. It is m/s².
  • (Higher tier) Mixing up inertia (a tendency, no unit) with inertial mass (a quantity measured in kg).

Revision questions

Try these, then check your answers below each one.

Question 1. A sprinter of mass 65 kg accelerates at 4.0 m/s² at the start of a race. Calculate the resultant force on the sprinter.

Answer: 260 N

Working: F = m a = 65 kg × 4.0 m/s² = 260 N.

Question 2. A resultant force of 2.4 kN acts on a car of mass 800 kg. Calculate the acceleration of the car.

Answer: 3 m/s²

Working: 2.4 kN = 2400 N. a = F ÷ m = 2400 N ÷ 800 kg = 3.0 m/s².

Question 3. A delivery van is travelling along a straight, level road at a constant velocity of 20 m/s. What is the resultant force on the van? (Choose from: Zero, Forwards, equal to the driving force, Forwards, larger than air resistance, Backwards, equal to air resistance.)

Answer: Zero

Working: The velocity is constant, so the acceleration is zero. By F = m a the resultant force is zero: the driving force is balanced by the resistive forces.

Related lessons

Continue in the full course

This lesson is section 10.1 (AGCPH1001) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

bottom of page