Edexcel IGCSE Physics: Double Science 复习笔记:1.1.1 Distance-Time Graphs

Edexcel IGCSE Physics: Double Science 复习笔记:1.1.1 Distance-Time Graphs

Distance-Time Graphs

 

  • A distance-time graph shows how the distance of an object moving in a straight line (from a starting position) varies over time:

5.6.8-Distance-Time-Graph-1

This graph shows a moving object moving further away from its origin

 

 

Constant Speed on a Distance-Time Graph

  • Distance-time graphs also show the following information:
    • If the object is moving at a constant speed
    • How large or small the speed is

     

  • straight line represents constant speed
  • The slope of the straight line represents the magnitude of the speed:
    • A very steep slope means the object is moving at a large speed
    • shallow slope means the object is moving at a small speed
    • flathorizontal line means the object is stationary (not moving)

     

 

5.6.8-Distance-Time-Graph-2

 

This graph shows how the slope of a line is used to interpret the speed of moving objects. Both of these objects are moving with a constant speed, because the lines are straight.

 

 

 

Changing Speed on a Distance-Time Graph

  • Objects might be moving at a changing speed
    • This is represented by a curve

     

  • In this case, the slope of the line will be changing
    • If the slope is increasing, the speed is increasing (accelerating)
    • If the slope is decreasing, the speed is decreasing (decelerating)

     

  • The image below shows two different objects moving with changing speeds

 

5.6.8-Distance-Time-Graph-3

 

Changing speeds are represented by changing slopes. The red line represents an object slowing down and the green line represents an object speeding up.

 

 

 

Gradient of a Distance-Time Graph

  • The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:

 

5.6.8-Speed-Gradient-EquationDistance-time-graph 

The speed of an object can be found by calculating the gradient of a distance-time graph

 

  • The rise is the change in y (distance) values
  • The run is the change in x (time) values

 

Worked Example

A distance-time graph is drawn below for part of a train journey. The train is travelling at a constant speed.5.6.8-WE-Gradient-of-D-T-question-graphCalculate the speed of the train.

 

Step 1: Draw a large gradient triangle on the graph and label the magnitude of the rise and run

    • The image below shows a large gradient triangle drawn with dashed lines
    • The rise and run magnitude is labelled, using the units as stated on each axes

     

 

5.6.8-WE-Gradient-of-D-T-solution-graph

 

 

Step 2: Convert units for distance and time into standard units

    • The distance travelled (rise) = 8 km = 8000 m
    • The time taken (run) = 6 mins = 360 s

     

 

Step 3: State that speed is equal to the gradient of a distance-time graph

    • The gradient of a distance-time graph is equal to the speed of a moving object:

     

 

5.6.8-Speed-Gradient-Equation

 

Step 4: Substitute values in to calculate the speed

 

speed = gradient = 8000 ÷ 360

 

speed = 22.2 m/s

 

Worked Example

Ose decides to take a stroll to the park. He finds a bench in a quiet spot and takes a seat, picking up where he left off reading his book on Black Holes.After some time reading, Ose realises he lost track of time and runs home.A distance-time graph for his trip is drawn below:5.6.8-WE-Ose-gets-carried-away-Question-imagea) How long does Ose spend reading his book?There are three sections labelled on the graph: A, B and C.b) Which section represents Ose running home?

c) What is the total distance travelled by Ose?

 

 

Part (a)

    • Ose spends 40 minutes reading his book
    • The flat section of the line (section B) represents an object which is stationary - so section B represents Ose sitting on the bench reading
    • This section lasts for 40 minutes - as shown in the graph below

     

5.6.8-WE-Ose-gets-carried-away-Ans-a

 

 

Part (b)

    • Section C represents Ose running home
    • The slope of the line in section C is steeper than the slope in section A
    • This means Ose was moving with a larger speed (running) in section C

     

 

Part (c)

 

    • The total distance travelled by Ose is 0.6 km
    • The total distance travelled by an object is given by the final point on the line - in this case, the line ends at 0.6 km on the distance axis. This is shown in the image below:

     

 

5.6.8-WE-Ose-gets-carried-away-Ans-c

Exam Tip

 

  • Use the entire line, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used - so remember to draw these directly on the graph itself!
  • Remember to check the units of variables measured on each axis. These may not always be in standard units - in our example, the unit of distance was km and the unit of time was minutes. Double-check which units to use in your answer.

转载自savemyexams

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