Equations of motion Revision Notes for AQA GCSE Physics

Equations of motion

Equations of motion help us work out how fast things are moving and how quickly they speed up or slow down. These equations are really useful for solving physics problems about moving objects.

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Understanding equations of motion is fundamental to physics as they allow us to predict and analyse the movement of objects in our everyday world, from cars on the road to athletes running on a track.

What is acceleration?

Acceleration tells us how quickly velocity changes over time. It measures how much faster or slower something gets each second.

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Key points about acceleration:

Acceleration is a vector quantity (this means it has direction)
We measure acceleration in metres per second squared (m/s²)
If acceleration is positive, the object speeds up
If acceleration is negative, the object slows down

The acceleration equation:

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

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Where:

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

What is velocity?

Velocity tells us how much distance something covers each second. It's different from speed because velocity includes direction.

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Key points about velocity:

Velocity is a vector quantity (has direction)
We measure velocity in metres per second (m/s)

The main velocity equation:

$v^2 = u^2 + 2as$

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Where:

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

You can also write this as: $v^2 - u^2 = 2as$

Typical acceleration values

Here are some everyday examples of acceleration:

Object	Acceleration (m/s²)
Athlete	8.5
Car	4
Lift	0.5
Rollercoaster	20

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Important fact: A falling object accelerates at 9.8 m/s² due to gravity. This is a constant value that you'll use frequently in physics calculations.

Worked example 1: finding acceleration

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Worked Example: Finding Acceleration

A cat speeds up from 2.5 m/s to 10.0 m/s in 3.0 seconds. What is its acceleration?

Given:

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

Step 1: Calculate change in velocity $\Delta v = v - u = 10.0 - 2.5 = 7.5$ m/s

Step 2: Apply the acceleration formula Using $a = \frac{\Delta v}{t}$ :

$a = \frac{7.5}{3.0} = 2.5 \text{ m/s}^2$

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

Worked example 2: finding final velocity

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Worked Example: Finding Final Velocity

A motorcycle starts at 4 m/s and accelerates at 2.4 m/s² for 200m. What is its final speed?

Given:

Initial velocity ( $u$ ) = 4 m/s
Acceleration ( $a$ ) = 2.4 m/s²
Distance ( $s$ ) = 200 m

Step 1: Apply the velocity equation Using $v^2 = u^2 + 2as$ :

$v^2 = 4^2 + (2 \times 2.4 \times 200)$

Step 2: Calculate step by step $v^2 = 16 + 960 = 976$

Step 3: Find the square root $v = \sqrt{976} = 31.2 \text{ m/s}$

Answer: The final velocity is 31.2 m/s

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Top tip: When you get $v^2$ , remember to find the square root to get the final velocity!

Important notes

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Critical Points to Remember:

If an object "starts from rest", its initial velocity ( $u$ ) is zero
Watch out for negative acceleration - this means the object is slowing down
Always check your units match the equation requirements

Remember!

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Key Points to Remember:

Acceleration measures how quickly velocity changes ( $a = \frac{\Delta v}{t}$ )
Velocity is distance per second and has direction
Both acceleration and velocity are vector quantities
The key equation is $v^2 = u^2 + 2as$ for finding final velocities
Falling objects accelerate at 9.8 m/s² due to gravity

Equations of motion (AQA GCSE Physics): Revision Notes