Equations of motion Revision Notes for AQA GCSE Physics Combined Science

Equations of motion

You can use special equations to work out how fast objects move and how quickly they speed up or slow down. These equations help us understand motion in physics and are fundamental tools for analysing the movement of objects around us.

What is acceleration?

Acceleration happens when something changes its speed. It tells us how much the velocity changes each second and is one of the most important concepts in physics.

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Key points about acceleration:

Acceleration is a vector quantity - this means it has both size and direction
It's measured in metres per second squared (m/s²)
The direction of acceleration can be the same as or opposite to the direction of motion

The acceleration equation:

$a = \frac{\Delta v}{t}$

Where:

$a$ = acceleration (m/s²)
$\Delta v$ = change in velocity (m/s)
$t$ = time taken (s)

This can also be written as: acceleration = change in velocity ÷ time taken

What is velocity?

Velocity is how fast something moves in a particular direction. It tells us how much distance changes each second and differs from speed because it includes direction.

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Key points about velocity:

Velocity is also a vector quantity - it has size and direction
It's measured in metres per second (m/s)
Unlike speed, velocity can be negative if the object moves in the opposite direction

Important velocity equation:

$v^2 - u^2 = 2as$

Where:

$v$ = final velocity (m/s)
$u$ = initial velocity (m/s)
$a$ = acceleration (m/s²)
$s$ = distance (m)

This equation links velocity, acceleration and distance together and is particularly useful when you don't know the time taken.

Typical acceleration values

Different objects have different accelerations depending on their design and the forces acting on them:

Object	Acceleration (m/s²)
Athlete	6.5
Car	4
Elevator	0.5
Rollercoaster	20

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Notice how rollercoasters have much higher acceleration values than everyday objects - this is what creates the thrilling sensation of being pushed back into your seat!

Free fall and terminal velocity

When objects fall through air, they don't keep speeding up forever. Two important concepts explain this behaviour:

Free fall:

Objects falling near Earth's surface accelerate at 9.8 m/s²
This happens when gravity is the only force acting on them
All objects fall at the same rate in free fall (ignoring air resistance)
This value is often called gravitational field strength or $g$

Terminal velocity:

As falling objects speed up, air resistance increases
Eventually, air resistance equals the weight of the object
The object then falls at a constant speed called terminal velocity
It stops accelerating because the forces are balanced

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At terminal velocity, acceleration becomes zero because the upward air resistance force exactly balances the downward gravitational force. This is why raindrops don't hurt when they hit you - they reach terminal velocity long before reaching the ground!

Working with the equations

Understanding how to apply these equations is crucial for solving motion problems effectively.

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Worked Example: Calculating Acceleration

A cat changes speed from 2.5 m/s to 10.0 m/s in 3.0 seconds. Calculate its acceleration.

Step 1: Identify what we know

Initial velocity ( $u$ ) = 2.5 m/s
Final velocity ( $v$ ) = 10.0 m/s
Time ( $t$ ) = 3.0 s

Step 2: Calculate change in velocity $\Delta v = v - u = 10.0 - 2.5 = 7.5$ m/s

Step 3: Apply the acceleration formula $a = \frac{\Delta v}{t} = \frac{7.5}{3.0} = 2.5$ m/s²

Answer: The cat's acceleration is 2.5 m/s²

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Important tip: When using these equations, if an object is slowing down (decelerating), the acceleration value will be negative. This indicates that the acceleration is in the opposite direction to the velocity.

Practice and problem-solving

When working with motion equations, always:

Identify what values you know and what you need to find
Choose the most appropriate equation for the given information
Pay careful attention to the direction of motion and signs
Check that your answer makes physical sense

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Key Points to Remember:

Acceleration equation: $a = \frac{\Delta v}{t}$ (change in velocity ÷ time)
Both velocity and acceleration are vector quantities - they have direction
The key motion equation: $v^2 - u^2 = 2as$ links velocity, acceleration and distance
Free fall acceleration on Earth is 9.8 m/s²
Terminal velocity occurs when air resistance equals weight, so acceleration becomes zero
Negative acceleration indicates the object is slowing down or accelerating in the opposite direction

Equations of motion (AQA GCSE Physics Combined Science): Revision Notes