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AQA A Level Maths: Mechanics復(fù)習(xí)筆記2.1.2 Velocity-Time Graphs

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年7月14日上午11:58

Velocity- time?graphs show the?velocity?of an object as it moves in a?straight line
They show?velocity?(on the vertical axis) against?time?(on the horizontal axis)
Velocity-time graphs can go?below the horizontal axis?whereas?speed-time graphs?can not

The?gradient?of the graph equals the?acceleration??of an object
A?straight line?shows that the object is?accelerating?at a?constant rate
A?horizontal?line shows that the object is moving at a?constant velocity
The?area?between graph and the x-axis tells us the?change in?displacement?of the object
- Graph?above?the x-axis means the object is moving?forwards
- Graph?below?the x-axis means the object is moving?backwards
The?total displacement?of the object from its starting point is the sum of the?areas above?the x-axis?minus?the sum of the?areas below?the x-axis
The?total distance travelled?by the object is the sum of?all?the?areas
If the graph?touches?the?x-axis?then the object is?stationary?at that time
If the graph is?above?the?x-axis?then the object has positive velocity and is?travelling forwards
If the graph is?below?the?x-axis?then the object has negative velocity and is?travelling backwards

2.1.2-Velocity-Time-Graphs-Diagram-1-1

2.1.2_WE_Velocity_Time-Graphs_1

(a) Calculate the acceleration of the bird at 20 seconds.

TEST-2.1.2-Velocity-Time-Graphs-Example-Solution-1-a

(b) Calculate the distance travelled in the first 28 seconds.

TEST-2.1.2-Velocity-Time-Graphs-Example-Solution-1-b

TEST-2.1.2-Velocity-Time-Graphs-Example-Solution-c

Be careful to spot if you are working with a distance-time graph or a velocity-time graph.
Be careful to spot if you are working with a speed-time graph or a velocity-time graph.
Check where the graph starts from on the y-axis, the velocity does not have to start at 0. For example, the scenario could be a car driving at a constant speed and the driver sees a hazard.
Be extra vigilant when working with negative gradients or with graphs under the x-axis, it is easy to make mistakes with these.
Speed is a scalar so it can?not?be negative whereas velocity can be.Make sure your units are consistent.

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