OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Motion: interpret enclosed area in velocity-time graphs (Higher tier only)
On a velocity-time graph the velocity axis is vertical and time is horizontal.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 10 of 14
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
On a velocity-time graph the velocity axis is vertical and time is horizontal. Splitting the region between the plotted line and the time axis into rectangles and triangles lets you find the enclosed area, and because velocity multiplied by time gives displacement, that area represents the displacement travelled in the chosen time interval. For a car accelerating steadily from rest to 20 m/s over 10 s, the area is a triangle: ½ × 10 s × 20 m/s = 100 m. For motion above the axis the displacement is positive; a region below the axis gives negative displacement, so areas on opposite sides must be subtracted to find the resultant displacement. Higher tier learners must read values from the axes, choose the correct shapes, keep units consistent and state what the area means rather than only a number.
What earns the marks
- Identifies the enclosed area as the displacement travelled during the time interval.
- Splits a compound region into rectangles and triangles before calculating each area.
- Multiplies velocity by time and keeps units consistent to give a displacement in metres.
- Treats area below the time axis as negative displacement and subtracts it from positive area.
Common mistakes and how to put them right
Reads the enclosed area as acceleration.
Put it right by recalling that the gradient gives acceleration while the area gives displacement.
Adds areas from above and below the axis without signs.
Put it right by subtracting the negative region to obtain resultant displacement.
Uses the wrong shape formula for a sloping section.
Put it right by using a triangle area of ½ × base × height for uniformly changing velocity.
Exam tips
- Read the axis scales carefully before choosing values, and note the unit of each axis.
- Sketch the split into simple shapes on the graph so each area is easy to check.
- State the meaning of the area as displacement, not just the numerical value.
- Watch for sections below the time axis and give them a negative sign.
Try the lesson
The start of the Motion: interpret enclosed area in velocity-time graphs (Higher tier only) lesson, made from checked teaching notes for this specification point.
Have a go first
A cyclist's velocity-time graph shows a constant velocity of 8 m/s for 5 s. What does the area enclosed between the graph line and the time axis represent, and what is its value?
Listen
On a velocity-time graph the velocity axis is vertical and time is horizontal. Splitting the region between the plotted line and the time axis into rectangles and triangles lets you find the enclosed area, and because velocity multiplied by time gives displacement, that area represents the displacement travelled in the chosen time interval. For a car accelerating steadily from rest to 20 m/s over 10 s, the area is a triangle: ½ × 10 s × 20 m/s = 100 m. For motion above the axis the displacement is positive; a region below the axis gives negative displacement, so areas on opposite sides must be subtracted to find the resultant displacement. Higher tier learners must read values from the axes, choose the correct shapes, keep units consistent and state what the area means rather than only a number. A strong answer earns marks for these points. Identifies the enclosed area as the displacement travelled during the time interval. Splits a compound region into rectangles and triangles before calculating each area. Multiplies velocity by time and keeps units consistent to give a displacement in metres. Treats area below the time axis as negative displacement and subtracts it from positive area. A common slip: Reads the enclosed area as acceleration. Instead, recalling that the gradient gives acceleration while the area gives displacement. Exam tip: Read the axis scales carefully before choosing values, and note the unit of each axis.
See it
Key words
Say what each word means before you turn the card.
Area as displacement
Try answering aloud or in your head before turning the card.
Velocity-time graph interpretation
Try answering aloud or in your head before turning the card.
Sign conventions for direction
Try answering aloud or in your head before turning the card.
See every definition
- Area as displacement
- The enclosed area between the plotted line and the time axis represents the displacement travelled in the chosen time interval, because velocity multiplied by time gives displacement.
- Velocity-time graph interpretation
- The velocity axis is vertical and time is horizontal, and the enclosed area is found by splitting the region between the plotted line and the time axis into rectangles and triangles.
- Sign conventions for direction
- Motion above the axis gives positive displacement, while a region below the axis gives negative displacement, so areas on opposite sides must be subtracted to find the resultant displacement.
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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