# P9 Motion AQA

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- Created by: wolf.dz7
- Created on: 24-11-17 19:38

## P9.1 Speed and distance-time graphs

- On distance-time graphs, a straight diagonal line sloping upwards represents constant speed, whilst a curved line represents acceleration or deceleration, and a straight horizontal line signifies that the object is stationary
- If it takes the same amount of time for the object to reach each equal distance, the object is moving at a constant speed, and so when drawing a graph it will be represented by a straight line
- The gradient (steepness of the line) determines the speed of the object - the larger the gradient, the faster the speed
- When an object is stationary, the line's gradient will be zero because it is a straight line and so the speed will also be zero because it is not moving
- When plotting points on a graph grid, make sure they are clear points or crosses, not large 'blobs'

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## P9.1 Speed and distance-time graphs (continued)

- When an object is moving at a constant speed, or to find an average speed, you can calculate the speed using this equation:

- As shown, this formula can be rearranged. It can be placed into a triangle to make it easier to remember:

- If the units of distance are metres (m) and the units of time are seconds (s), the units of speed will be metres per second (m/s)
- Always convert the time into seconds and the distance into metres if they are written in any other measurement

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## P9.2 Velocity and acceleration

- Velocity – speed in a given direction
- An object that travels at constant velocity travels at a constant speed, without changing its direction, so it travels in a straight line in a given direction
- Two moving objects can have the same speed but different velocities (for example, two things moving at the same speed, but one travelling north and the other south will have different velocities)
- An object moving round in a circle has a direction of motion that changes continuously as it moves around, meaning that even if its speed is constant its velocity is not, for instance, a car moving around a roundabout
- Displacement – the distance travelled in a given direction
- Acceleration - an object's change in velocity per second
- Deceleration (or negative acceleration) – when an object decreases in speed
- A minus value for acceleration means that the object is decelerating, but when talking about deceleration, you don't need to include the minus sign
- Any object with a changing velocity is accelerating
- The units of acceleration are metres per second squared (m/s^2), if the units of time are seconds (s) and the units of velocity are metres per second (m/s)
- (m/s^2 means m/s/s, which is the change in speed measured in m/s that occurs every second)

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## P9.2 Velocity and acceleration (continued)

- The following formula can be used to work out the average acceleration:

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- This can be placed in a triangle to help with rearranging the formula, as shown:

- Also, the change in velocity is equal to the final velocity minus the initial velocity, so the formula can also be written like this:

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## P9.3 More about velocity-time graphs

- On a velocity-time graph, when the line slopes up it shows that the object involved is accelerating
- When it slopes down, the object is decelerating
- When the line is horizontal, the object is moving at a constant speed, or, if the line is across the x-axis then it is stationary
- The gradient of the line on a velocity-time graph represents acceleration
- When drawing a straight line graph, always use a ruler
- Acceleration and deceleration changes the velocity of an object, meaning that on the graph it will be represented as a diagonal line
- When the gradient of the line is positive (the line slopes upwards), the acceleration will also be positive, so when it is negative (the line slopes downwards), the acceleration is negative too, meaning that it represents deceleration.

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## P9.3 More about velocity-time graphs (continued)

- The area under the line on a velocity-time graph represents the distance travelled in a given direction (or displacement)

- If you find the area of the darker blue rectangle on the graph and add it to the area of the light blue triangle, the answer will be the displacement
- Speed and velocity don’t have to be in m/s but can also be in km/h
- However, if plotted on a graph or used in an equation, km/h must be converted to m/s

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## P9.4 Analysing motion graphs

- On a distance-time graph, the speed of the object is represented by the gradient of the line
- Therefore, to work out the speed, you will need to work out the gradient by drawing two lines to form a triangle on the graph:

- When the object is changing speed, the line will be curved, so you will need to draw a tangent (a straight line that touches the curve without cutting through it) at a certain point on the x-axis of the graph (in this case on 6 seconds), as shown in the graph below:

Gradient = height base = 120m 5s = 24m/s = speed

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## P9.4 Analysing motion graphs (continued)

- To calculate the acceleration using a velocity-time graph, you can use the same method as working out the speed from a distance-time graph
- The gradient of the line on a velocity-time graph represents acceleration
- You will need to draw two straight lines to form a triangle and divide the height of the triangle by the base of the triangle, to find the acceleration

Gradient = height base = 30m/s 10s = 3m/s^2 = acceleration

Overall:

- The speed of an object moving at constant speed is given by the gradient of the line on its distance-time graph
- The speed of an object moving at non-constant speed can be found by drawing a tangent from a certain point and calculating the gradient on that line
- The acceleration of an object is given by the gradient of the line on its velocity-time graph

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## Key definitions

- The gradient (steepness of the line) determines the speed of the object - the larger the gradient, the faster the speed
- Velocity – speed in a given direction
- Displacement – the distance travelled in a given direction
- Acceleration - an object's change in velocity per second
- Deceleration (or negative acceleration) – when an object decreases in speed
- Tangent - a straight line that touches a curved line on a distance-time graph without cutting through it, which you can use to find the gradient of the line at a certain point on the x-axis of the graph

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## Key formulae

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