AQA · GCSE · Physics
Course version: 8463 · Version from Sept 2016
(HT only) measure, when appropriate, the area under a velocity–time graph…
Full specification wording
Acceleration: (HT only) measure, when appropriate, the area under a velocity–time graph by counting squares.
On a velocity–time graph, the area between the line and the time axis represents distance travelled.
Checked against the AQA 8463 specification (opens in a new tab) on .
- Point 20 of 23
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
On a velocity–time graph, the area between the line and the time axis represents distance travelled. When the line is curved or made of several straight sections, you can find this area by counting squares on the grid. First work out what one square is worth: multiply the velocity represented by one square's height by the time represented by one square's width. For example, if one square is 2 m/s tall and 0.5 s wide, each square is 1 m of distance. Count whole squares under the line, then combine part-squares to make whole ones. Multiply the total number of squares by the value of one square to give the distance. This method is appropriate when the area is not a simple triangle or rectangle, and it estimates distance from the graph.
What earns the marks
- State that the area under a velocity–time graph equals the distance travelled.
- Calculate the distance represented by one grid square by multiplying its velocity interval by its time interval.
- Count whole squares beneath the line and combine partial squares to estimate the total number of squares.
- Multiply the total number of squares by the distance value of one square to obtain the distance.
- Show working clearly, including the value of one square and the square count, so the method can be followed.
Common mistakes and how to put them right
Counting squares above the line instead of the area between the line and the time axis.
Put it right by shading the region under the line before counting.
Forgetting to convert the square count into a distance.
Put it right by multiplying by the distance represented by one square.
Treating every partial square as a whole square.
Put it right by pairing partial squares to make whole squares or estimating fractions carefully.
Exam tips
- Label the axes with their quantities and units before reading any values from the graph.
- Write down the value of one square in metres before counting, so the final multiplication is clear.
- Check that the final answer has the unit of distance, such as metres or kilometres, and is reasonable for the motion shown.
Try the lesson
The start of the Acceleration: (HT only) measure, when appropriate, the area under a velocity–time graph by counting squares. lesson, made from checked teaching notes for this specification point.
Have a go first
A student is analysing a velocity–time graph where the line is a curve. Which method is most appropriate to estimate the area under the graph?
Listen
On a velocity–time graph, the area between the line and the time axis represents distance travelled. When the line is curved or made of several straight sections, you can find this area by counting squares on the grid. First work out what one square is worth: multiply the velocity represented by one square's height by the time represented by one square's width. For example, if one square is 2 m/s tall and 0.5 s wide, each square is 1 m of distance. Count whole squares under the line, then combine part-squares to make whole ones. Multiply the total number of squares by the value of one square to give the distance. This method is appropriate when the area is not a simple triangle or rectangle, and it estimates distance from the graph. A strong answer earns marks for these points. State that the area under a velocity–time graph equals the distance travelled. Calculate the distance represented by one grid square by multiplying its velocity interval by its time interval. Count whole squares beneath the line and combine partial squares to estimate the total number of squares. Multiply the total number of squares by the distance value of one square to obtain the distance. A common slip: Counting squares above the line instead of the area between the line and the time axis. Instead, shading the region under the line before counting. Exam tip: Label the axes with their quantities and units before reading any values from the graph.
See it
Put it in order
Put these steps in the order they happen.
- 1. Count whole squares beneath the line
- 2. Work out what one square is worth: velocity per square height × time per square width
- 3. Area under a velocity–time graph equals distance travelled
- 4. Distance travelled
- 5. Multiply total number of squares by the value of one square
- 6. Combine part-squares to make whole ones
Key words
Say what each word means before you turn the card.
Area under a velocity–time graph
Try answering aloud or in your head before turning the card.
Counting squares
Try answering aloud or in your head before turning the card.
Value of one square
Try answering aloud or in your head before turning the card.
Partial squares
Try answering aloud or in your head before turning the card.
See every definition
- Area under a velocity–time graph
- The region between the line and the time axis, which represents distance travelled.
- Counting squares
- A method of finding the area under a curved or multi-section line by counting squares on the grid.
- Value of one square
- The velocity represented by one square's height multiplied by the time represented by one square's width.
- Partial squares
- Squares under the line that are not whole, which are combined to make whole ones when counting.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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