CIE A Level Maths: Mechanics复习笔记2.1.2 Velocity-Time Graphs

Velocity-Time Graphs

What is a velocity-time graph?

  • 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

What are the key features of a velocity-time graph?

  • The gradient of the graph equals the acceleration  of an object
  • straight line shows that the object is accelerating at a constant rate
  • 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

Worked Example

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

(c) Calculate the displacement of the bird from its starting point after 60 seconds.

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

Exam Tip

  • 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.

 

 

 

 

转载自savemyexams

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