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GCSE Physics Revision

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GCSE Physics revision

Newton's Second Law

Forces, accelerations and Newton's Laws of motion

AQA 4.5.6.2.2
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AQA student objectives

Learning pathway

All · Most · Some

ALL 🎯

Explain inertial mass as an object’s resistance to changes in velocity and calculate it as force divided by acceleration (m = F/a).

MOST 🎯🎯

Apply the scientific explanation of newton's second law to a relevant example.

SOME 🎯🎯🎯

Analyse a new situation involving newton's second law and explain the scientific reasoning.

Revision summary

Key knowledge

Read on screen, then print for Cornell-style active revision.

What is Acceleration?

  • Acceleration is the rate of change in velocity — in other words, how quickly an object speeds up or slows down.
  • Acceleration is measured in metres per second squared (m/s2 ).
  • Like velocity, acceleration is a vector quantity, meaning it has both magnitude and direction.

The First Acceleration Equation

  • Δv
  • The first key equation is a = t , where a is acceleration, Δv is the change in velocity, and t is time.
  • The symbol Δ (delta) means 'change in', so Δv represents the change in velocity.
  • Change in velocity can also be written as v − u, where v is the final velocity and u is the initial velocity.
  • Use this equation when the question provides time rather than distance.

Worked Example: Car Accelerating

  • If a car accelerates from 15 m/s to 35 m/s in 5 seconds, the change in velocity is
  • 35 − 15 = 20 m/s.
  • Dividing the change in velocity by time gives a = 20
  • 5
  • = 4 m/s2 .
  • 2
  • This value of 4 m/s represents the average acceleration over the 5-second period.

Average vs. Uniform Acceleration

  • In real life, an object's acceleration may vary over time, so a calculated value is often the average acceleration.
  • If an object accelerates at the same rate throughout its journey, this is called uniform or constant acceleration.
  • Negative acceleration indicates that the object is slowing down, which is also known as deceleration.

The Second Acceleration Equation

  • The second key equation is v 2 − u2 = 2as, where s is the distance travelled in metres.
  • Use this equation when the question gives distance instead of time.
  • If an object starts from rest (stationary), its initial velocity u = 0 m/s, which simplifies the equation.

Worked Example: Ball Dropped from a Height

  • A ball dropped from rest has an initial velocity of u = 0 m/s and accelerates downwards at g = 9.8 m/s2 due to gravity.
  • If the ball's final velocity just before hitting the ground is v = 7 m/s, we can rearrange
  • 2 2
  • −u the equation to find distance: s = v 2a .
  • 2 2
  • 49
  • Substituting the values gives s = 72×9.8
  • −0
  • = 19.6
  • = 2.5 m, so the ball was dropped from 2.5 m above the ground.

Choosing the Right Equation

  • If a question provides time, use a = v−u t to find acceleration.
  • If a question provides distance, use v 2 − u2 = 2as instead.
  • Always check whether the object starts from rest, as this means u = 0, which simplifies your calculation.

Newton's First Law Recap

  • An object with a resultant force of zero will remain stationary or continue moving at the same velocity (same speed and direction).
  • A resultant force that is not zero will cause an object's velocity to change, leading into Newton's Second Law.

Newton's Second Law of Motion

  • Newton's Second Law states that the acceleration of an object is proportional to the resultant force acting on it.
  • The acceleration of an object is inversely proportional to its mass, meaning a larger mass results in a smaller acceleration for the same force.
  • If the resultant force is doubled whilst mass stays the same, the acceleration also doubles.
  • If the mass is doubled whilst the resultant force stays the same, the acceleration is halved.

The Force Equation

  • The equation linking force, mass, and acceleration is F = m × a, where force is in Newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²).
  • This equation must be memorised as it is not provided in the GCSE exam.
  • To find acceleration, rearrange the equation to a = F / m, and to find mass, use m = F / a.

Worked Example: Calculating Force

  • To calculate the force needed to accelerate a 5 kg object at 4 m/s², substitute into F = m × a to get F = 5 × 4 = 20 N.

Worked Example: Calculating Acceleration

  • To find the acceleration of a 0.25 kg object with a 50 N force applied, use a = F / m = 50 / 0.25 = 100 m/s².

Estimating Speed, Acceleration & Forces in Road Transport

  • A typical car travels at approximately 13 m/s on a main road and around 30 m/s on a motorway in the UK.
  • A typical acceleration for a car moving from a main road to a motorway is approximately 2 m/s².
  • The force required to achieve this acceleration for a typical family car is approximately 2,000 N.

Inertia (Higher Tier)

  • Inertia is the property of an object that causes it to remain stationary or continue moving at the same velocity unless a resultant force acts upon it.
  • Inertial mass is a measure of how difficult it is to change the velocity of an object.
  • Inertial mass is defined as the ratio of the force applied to the acceleration produced: Inertial mass = F / a.
  • An object with a large inertial mass requires a greater force to produce the same acceleration compared to an object with a smaller inertial mass.