Difference between revisions of "Distance-Time Graph"
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{| class="wikitable" | {| class="wikitable" | ||
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| − | |[[File: | + | |[[File:dtGraphCalculation4.png|center|300px]] |
| − | |[[File: | + | |[[File:dtGraphCalculation5.png|center|300px]] |
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| − | | style="height:20px; width:300px; text-align:left;" |'''Calculate the speed of the object in | + | | style="height:20px; width:300px; text-align:left;" |'''Calculate the [[speed]] of the object in the first 10 seconds of the journey.''' |
| + | : distance = 200[[m]] | ||
| + | : time = 10[[s]] | ||
| + | :<math>v= {\frac{distance}{time}} </math> | ||
| + | :<math>Speed = {\frac{200}{10}} </math> | ||
| + | :<math>Speed = 20m/s </math> | ||
| + | | style="height:20px; width:300px; text-align:left;" |'''Calculate the [[speed]] of the object in the first 10 seconds of the journey.''' | ||
| + | : distance = 70[[m]] | ||
| + | : time = 10[[s]] | ||
| + | :<math>Speed = {\frac{distance}{time}} </math> | ||
| + | :<math>Speed = {\frac{70}{10}} </math> | ||
| + | :<math>Speed = 7m/s </math> | ||
| + | |} | ||
| + | |||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | |[[File:dtGraphCalculation4.png|center|300px]] | ||
| + | |[[File:dtGraphCalculation5.png|center|300px]] | ||
| + | |- | ||
| + | | style="height:20px; width:300px; text-align:left;" |'''Calculate the average [[speed]] of the [[object]] over the entire journey.''' | ||
: distance = 400[[m]] | : distance = 400[[m]] | ||
: time = 80[[s]] | : time = 80[[s]] | ||
| − | :<math> | + | :<math>v= {\frac{distance}{time}} </math> |
| − | :<math>Speed = {\ | + | :<math>Speed = {\frac{400}{80}} </math> |
:<math>Speed = 5m/s </math> | :<math>Speed = 5m/s </math> | ||
| − | | style="height:20px; width:300px; text-align:left;" |'''Calculate the | + | | style="height:20px; width:300px; text-align:left;" |'''Calculate the average [[speed]] of the [[object]] over the entire journey.''' |
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: distance = 500[[m]] | : distance = 500[[m]] | ||
: time = 80[[s]] | : time = 80[[s]] | ||
| − | :<math>Speed = {\ | + | :<math>Speed = {\frac{distance}{time}} </math> |
| − | :<math>Speed = {\ | + | :<math>Speed = {\frac{500}{80}} </math> |
:<math>Speed = 6.25m/s </math> | :<math>Speed = 6.25m/s </math> | ||
|} | |} | ||
Revision as of 10:42, 14 February 2019
Contents
Key Stage 3
Meaning
A distance time graph is a graph that shows how the distance of an object from the origin changes with time.
About Distance Time Graphs
- Distance-time graphs give information about the journey taken by an object.
- On a distance time graph the distance is plotted on the y-axis and the time is plotted on the x-axis.
- A distance time graph can be used to calculate the speed of an object.
| Slow Speed | Medium Speed | High Speed |
 |
 |
 |
| A constant speed is shown by a constant positive gradient. | A higher gradient means a higher speed. | The highest speed is shown by the steepest gradient. |
| Stationary | Accelerating | Decelerating |
 |
 |
 |
| A gradient of zero shows the object is not moving. | Acceleration is shown by an increasing gradient. | Deceleration is shown by a decreasing gradient. |
Example Calculations
- The speed can be calculated from a distance time graph by reading the graph and using the equation Speed=Distance/Time.
 |
 |
| Calculate the speed of the object in this 80 second journey.
\[Speed = {\tfrac{distance}{time}} \] \[Speed = {\tfrac{400}{80}} \] \[Speed = 5m/s \] |
Calculate the speed of the object in the first 20 seconds.
\[Speed = {\tfrac{distance}{time}} \] \[Speed = {\tfrac{400}{20}} \] \[Speed = 20m/s \] |
|
|
| Calculate the speed of the object between 20 and 80 seconds.
\[Speed = {\tfrac{distance}{time}} \] \[Speed = {\tfrac{100}{60}} \] \[Speed \approx 1.7m/s \] |
Calculate the average speed of the object for its journey.
\[Speed = {\tfrac{distance}{time}} \] \[Speed = {\tfrac{500}{80}} \] \[Speed = 6.25m/s \] |
Key Stage 4
Meaning
A distance time graph is a graph that shows how the distance of an object from the origin changes with time.
About Distance Time Graphs
- Distance-time graphs give information about the journey taken by an object.
- On a distance time graph the distance is plotted on the y-axis and the time is plotted on the x-axis.
- A distance time graph can be used to calculate the speed of an object.
| Slow Speed | Medium Speed | High Speed |
|
|
|
| A constant speed is shown by a constant positive gradient. | A higher gradient means a higher speed. | The highest speed is shown by the steepest gradient. |
| Stationary | Accelerating | Decelerating |
|
|
|
| A gradient of zero shows the object is not moving. | Acceleration is shown by an increasing gradient. | Deceleration is shown by a decreasing gradient. |
Example Calculations
- The speed can be calculated from a distance time graph by reading the graph and using the equation Speed=Distance/Time.
 |
 |
| Calculate the speed of the object in the first 10 seconds of the journey.
\[v= {\frac{distance}{time}} \] \[Speed = {\frac{200}{10}} \] \[Speed = 20m/s \] |
Calculate the speed of the object in the first 10 seconds of the journey.
\[Speed = {\frac{distance}{time}} \] \[Speed = {\frac{70}{10}} \] \[Speed = 7m/s \] |
|
|
| Calculate the average speed of the object over the entire journey.
\[v= {\frac{distance}{time}} \] \[Speed = {\frac{400}{80}} \] \[Speed = 5m/s \] |
Calculate the average speed of the object over the entire journey.
\[Speed = {\frac{distance}{time}} \] \[Speed = {\frac{500}{80}} \] \[Speed = 6.25m/s \] |