OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Apply: (final velocity (m/s))² – (initial velocity (m/s))² = 2 ×…
Full specification wording
Motion: apply: (final velocity (m/s))² – (initial velocity (m/s))² = 2 × acceleration (m/s²) × distance (m)
This equation links velocity, acceleration and distance for motion with constant acceleration, without needing the time.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 3 of 14
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
This equation links velocity, acceleration and distance for motion with constant acceleration, without needing the time. Square the final velocity and subtract the square of the initial velocity; this equals twice the acceleration multiplied by the distance travelled. For example, a cyclist accelerating at 2 m/s² from rest over 9 m reaches v² = 0² + 2 × 2 × 9 = 36, so v = 6 m/s. To find distance, divide the difference of the squared velocities by twice the acceleration. Check units: (m/s)² and m/s² × m both give m²/s². In a multiple-choice question, square the velocities before subtracting, then take the square root if the option is a velocity rather than a squared value.
What earns the marks
- Selects the option obtained by squaring the final and initial velocities, subtracting, and equating to twice acceleration times distance.
- Squares each velocity before subtracting rather than subtracting the velocities first.
- Takes the square root when the required answer is a final velocity rather than a squared value.
- Rearranges correctly to find distance as the difference of squared velocities divided by twice the acceleration.
- Confirms that both sides of the equation carry the unit m²/s².
Common mistakes and how to put them right
Subtracts the velocities before squaring.
Put it right: Square each velocity first, then subtract.
Forgets to double the acceleration when multiplying by distance; use 2 × a × s.
Reports a squared velocity when the option asks for velocity.
Put it right: Take the square root of the result.
Exam tips
- Write the equation, then substitute values one at a time to avoid order errors.
- Square the velocities before subtracting, and keep the subtraction in the stated order.
- Check whether the question wants a velocity or a squared velocity before choosing an option.
Try the lesson
The start of the Motion: apply: (final velocity (m/s))² – (initial velocity (m/s))² = 2 × acceleration (m/s²) × distance (m) lesson, made from checked teaching notes for this specification point.
Have a go first
A car starts from rest and accelerates at 2 m/s² over a distance of 9 m. Using v² − u² = 2 × a × s, what is its final velocity?
Listen
This equation links velocity, acceleration and distance for motion with constant acceleration, without needing the time. Square the final velocity and subtract the square of the initial velocity; this equals twice the acceleration multiplied by the distance travelled. For example, a cyclist accelerating at 2 m/s² from rest over 9 m reaches v² = 0² + 2 × 2 × 9 = 36, so v = 6 m/s. To find distance, divide the difference of the squared velocities by twice the acceleration. Check units: (m/s)² and m/s² × m both give m²/s². In a multiple-choice question, square the velocities before subtracting, then take the square root if the option is a velocity rather than a squared value. A strong answer earns marks for these points. Selects the option obtained by squaring the final and initial velocities, subtracting, and equating to twice acceleration times distance. Squares each velocity before subtracting rather than subtracting the velocities first. Takes the square root when the required answer is a final velocity rather than a squared value. Rearranges correctly to find distance as the difference of squared velocities divided by twice the acceleration. Exam tip: Write the equation, then substitute values one at a time to avoid order errors.
Key words
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Velocity–acceleration–distance relationship
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Squaring velocities before subtraction
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Constant acceleration motion
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Unit consistency of m²/s²
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See every definition
- Velocity–acceleration–distance relationship
- The equation states that the square of the final velocity minus the square of the initial velocity equals twice the acceleration multiplied by the distance.
- Squaring velocities before subtraction
- Each velocity is squared first, then the square of the initial velocity is subtracted from the square of the final velocity.
- Constant acceleration motion
- Motion for which the equation links velocity, acceleration and distance without needing the time.
- Unit consistency of m²/s²
- Both (m/s)² and m/s² × m give m²/s², so both sides of the equation carry the same unit.
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