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P10.1 Forces and Acceleration

GCSE Combined Science · AQA · Chapter P10: Force and Motion

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: newton’s first and second laws, using F = m a, estimating road-transport forces 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
  • Estimate the accelerations and forces involved for everyday road vehicles
  • (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 ∝.
  • 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

To predict how an object moves, add the forces on it, 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 parked bus has its weight balanced by the push of the road.
  • A moving object keeps moving at the same speed in the same direction. A spacecraft far from any star, with no forces on it, coasts in a straight line at a steady speed; a car cruising at a steady 30 m/s has its driving force 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

Worked example: force on a go-kart

A go-kart and its driver have a total mass of 160 kg. They accelerate at 2.5 m/s². Calculate the resultant force.
F = m a = 160 kg × 2.5 m/s²

Answer: F = 400 N

Worked example: finding the resultant first

A 1500 kg car has a driving force of 1350 N and resistive forces of 900 N. Calculate its acceleration.
resultant force = 1350 − 900 = 450 N forwards; a = F ÷ m = 450 ÷ 1500

Answer: a = 0.30 m/s² forwards

Rearranging, units and estimates

Worked example: finding acceleration

A toy car of mass 400 g has a resultant force of 0.18 N on it. Calculate its acceleration.
Convert: 400 g = 400 ÷ 1000 = 0.400 kg; a = F ÷ m = 0.18 N ÷ 0.400 kg

Answer: a = 0.45 m/s²

Worked example: finding mass

A resultant force of 6.3 kN gives a van an acceleration of 2.1 m/s². Calculate the mass of the van.
Convert: 6.3 kN = 6300 N; m = F ÷ a = 6300 N ÷ 2.1 m/s²

Answer: m = 3000 kg

Worked example: estimating for a family car

A family car has a mass of about 1300 kg and can reach about 25 m/s from rest in about 10 s.
a = change in velocity ÷ time ≈ 25 ÷ 10 = 2.5 m/s²; F = m a ≈ 1300 × 2.5 ≈ 3300 N

Answer: a resultant force of roughly 3 kN

Exam tip: Change grams to kilograms (÷ 1000) and kilonewtons to newtons (× 1000) before you substitute into F = m a. The acceleration is always in the same direction as the resultant force: if the resultant force is opposite to the motion, the object decelerates.

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 passenger standing on a bus lurches backwards when it pulls away suddenly, and a bag on a car seat slides forwards when the car brakes hard. A fully loaded oil tanker takes many minutes to stop.

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 two boxes

The same 9.0 N push acts on two identical-looking boxes on a low-friction surface. Box P accelerates at 4.5 m/s²; box Q at 1.8 m/s².
P: m = 9.0 ÷ 4.5 = 2.0 kg Q: m = 9.0 ÷ 1.8 = 5.0 kg
Q has the larger inertial mass, so its velocity is harder to change – it must be the full box.

Answer: 2.0 kg and 5.0 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 cyclist and her bicycle have a total mass of 72 kg. They accelerate at 1.5 m/s². Calculate the resultant force.

Answer: 108 N

Working: F = m a = 72 kg × 1.5 m/s² = 108 N.

Question 2. A resultant force of 3.3 kN acts on a car of mass 1100 kg. Calculate the acceleration of the car.

Answer: 3 m/s²

Working: 3.3 kN = 3300 N. a = 3300 ÷ 1100 = 3.0 m/s².

Question 3. A delivery van travels along a straight, level road at a constant velocity of 22 m/s. What is the resultant force on the van? (Choose from: Zero, Equal to the driving force, Equal to its weight, A small force forwards.)

Answer: Zero

Working: The velocity is constant, so the acceleration is zero and, by Newton’s first law, the resultant force is zero: the driving force balances the resistive forces.

Related lessons

Continue in the full course

This lesson is section P10.1 (AGCSC3901) of our free GCSE Combined Science 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 Combined Science course.

 

 

 

 

 

 

 

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