CIE A Level Maths: Mechanics复习笔记2.1.1 Displacement-Time Graphs

Displacement-Time Graphs

What is a displacement-time graph?

  • Displacement-time graphs show the displacement of an object from a fixed origin as it moves in a straight line
  • They show displacement (on the vertical axis) against time (on the horizontal axis)
  • Displacement-time graphs can go below the horizontal axis whereas distance-time graphs can not
    • Distance can not be negative whereas displacement can be

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

  • The gradient of the graph equals the velocity of the object
    • positive gradient means the object is travelling forwards
    • A negative gradient means that the object is travelling backwards
    • The steeper the line, the greater the speed
  • straight line shows that the object is moving at a constant velocity
  • curved line shows that the object is accelerating or decelerating
  • horizontal line shows that the object is stationary
  • If the graph touches the x-axis, then the object is at the origin at that time

2-1-1-displacement-time-graphs-diagram-1

How do I find the average speed and the average velocity of a journey?

Worked Example

2.1.1-_WE_Displacement-Time-Graphs_1

(a)   Calculate the velocity of the athlete during the first 2 seconds.

2-1-1-displacement-time-graphs-example-solution-1-a

(b)    Describe the motion of the athlete between the times of 2 seconds and 5 seconds.

2-1-1-displacement-time-graphs-example-solution-1-b

(c)   Calculate the velocity of the athlete at 10 seconds.

2-1-1-displacement-time-graphs-example-solution-c

(d)   Find the total distanced travelled by the athlete during the 14 seconds.

2-1-1-displacement-time-graphs-example-solution-d

Exam Tip

  • Be careful to spot if you are working with a displacement-time graph or a velocity-time graph.
  • Be careful to spot if you are working with a displacement-time graph or a distance-time graph
  • Check where the graph starts from on the y-axis, the object does not have to start at 0. For example, if the graph starts at 100, the scenario could be a student on a walk starting 100 m from their house.
  • Distance is a scalar so it can not be negative whereas displacement from a starting point can be.
  • Think about the units when calculating, make sure they are consistent.

 

 

 

 

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