CIE A Level Maths: Mechanics复习笔记2.1.3 Drawing Travel Graphs

Drawing Travel Graphs

How do I draw a displacement-time graph or a velocity-time graph?

  • You may be asked to draw a displacement-time graph or a velocity-time graph
  • You will be given information about different sections of a journey and must draw each section and label the points on the axes
  • Remember that time will always be on the x-axis
  • Always remember to include units when you label the axis
  • Use appropriate facts about the gradient and area under the graph to work backwards and find relevant or missing information
    • The gradient of a displacement-time graph is the velocity and the gradient of a velocity-time graph is the acceleration
    • The area between a velocity-time graph and the x-axis is the displacement

2-1-3-drawing-travel-graphs-diagram-1-1

2-1-3-drawing-travel-graphs-diagram-1-2

Worked Example

(a)  Sketch a velocity-time graph to show the motion of the train.

hJKsbARD_2-1-3-drawing-travel-graphs-example-solution-a

(b)Find the deceleration of the train from the moment the brakes were first applied to the moment its speed first reached 12 m s-1.

2-1-3-drawing-travel-graphs-example-solution-b

(c)Calculate the total time from the moment the brakes were first applied to the moment the train came to rest.

2-1-3-drawing-travel-graphs-example-solution-c

Exam Tip

  • As in the worked example, examiners can use other words, such as uniformly, to mean constant.
  • Be careful to spot if you are working with a displacement-time graph or a velocity-time graph.
  • Remember that displacement and velocity can be negative whereas distance and speed can not be negative.
  • Take care when a velocity-time graph is below the x-axis, if it has a negative gradient then it is speeding up and moving backwards. If it has a positive gradient below the x-axis then it is still moving backwards but it is slowing down.
  • Think about the units when calculating displacement, velocity and acceleration.

 

 

 

 

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