OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(i) the equations of motion for constant acceleration in a straight line,…
Full specification wording
Linear motion: (i) the equations of motion for constant acceleration in a straight line, including motion of bodies falling in a uniform gravitational field without air resistance: v = u + at, s = 1/2(u + v)t, s = ut + 1/2 at², v² = u² + 2as
For constant acceleration in a straight line, four equations link initial velocity u, final velocity v, acceleration a, displacement s and time t: v = u + at, s = 1/2(u + v)t, s = ut + 1/2 at²,…
Checked against the OCR H556 specification (opens in a new tab) on .
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- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
For constant acceleration in a straight line, four equations link initial velocity u, final velocity v, acceleration a, displacement s and time t: v = u + at, s = 1/2(u + v)t, s = ut + 1/2 at², and v² = u² + 2as. Each equation omits one quantity, so choose the one that matches the data and the unknown. For a body falling in a uniform gravitational field without air resistance, take a = g, approximately 9.81 m s⁻² downwards, and define a positive direction consistently. For example, a ball dropped from rest for 2.0 s has v = 0 + 9.81 × 2.0 = 19.62 m s⁻¹ and s = 0 × 2.0 + 1/2 × 9.81 × (2.0)² = 19.62 m. Always check units and the sign of each vector.
What earns the marks
- The equation v = u + at links final velocity, initial velocity, acceleration and time, and is used when displacement is not required.
- The equation s = 1/2(u + v)t links displacement, initial and final velocities and time, and is used when acceleration is not required.
- The equation s = ut + 1/2 at² links displacement, initial velocity, acceleration and time, and is used when final velocity is not required.
- The equation v² = u² + 2as links final velocity, initial velocity, acceleration and displacement, and is used when time is not required.
- For a body falling in a uniform gravitational field without air resistance, acceleration is g, approximately 9.81 m s⁻², and a consistent positive direction must be chosen.
Common mistakes and how to put them right
Using an equation that contains the unknown quantity.
Put it right: Select the equation that omits the unmeasured quantity.
Forgetting that the equations apply only for constant acceleration in a straight line.
Put it right: Check the conditions first.
Mixing up u and v or omitting a sign.
Put it right: Define a positive direction and label u and v carefully.
Using g = 9.81 m s⁻² without direction or with the wrong sign.
Put it right: Assign the sign of g according to the chosen positive direction.
Exam tips
- List the known quantities with their symbols and units, then choose the equation that contains the unknown and the knowns.
- Define a positive direction before substituting, especially for falling bodies, and keep the sign of g consistent.
- Substitute values only after rearranging the equation, and check that the final unit matches the quantity required.
Try the lesson
The start of the Linear motion: (i) the equations of motion for constant acceleration in a straight line, including motion of bodies falling in a uniform gravitational field without air resistance: v = u + at, s = 1/2(u + v)t, s = ut + 1/2 at², v² = u² + 2as lesson, made from checked teaching notes for this specification point.
Listen
For constant acceleration in a straight line, four equations link initial velocity u, final velocity v, acceleration a, displacement s and time t: v = u + at, s = 1/2(u + v)t, s = ut + 1/2 at², and v² = u² + 2as. Each equation omits one quantity, so choose the one that matches the data and the unknown. For a body falling in a uniform gravitational field without air resistance, take a = g, approximately 9.81 m s⁻² downwards, and define a positive direction consistently. For example, a ball dropped from rest for 2.0 s has v = 0 + 9.81 × 2.0 = 19.62 m s⁻¹ and s = 0 × 2.0 + 1/2 × 9.81 × (2.0)² = 19.62 m. Always check units and the sign of each vector. A strong answer earns marks for these points. The equation v = u + at links final velocity, initial velocity, acceleration and time, and is used when displacement is not required. The equation s = 1/2(u + v)t links displacement, initial and final velocities and time, and is used when acceleration is not required. The equation s = ut + 1/2 at² links displacement, initial velocity, acceleration and time, and is used when final velocity is not required. The equation v² = u² + 2as links final velocity, initial velocity, acceleration and displacement, and is used when time is not required. A common slip: Using an equation that contains the unknown quantity: the error is choosing an equation that includes both the required unknown and an unmeasured quantity. Instead, select the equation that omits the unmeasured quantity. Exam tip: List the known quantities with their symbols and units, then choose the equation that contains the unknown and the knowns.
See it
Key words
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Constant acceleration equations
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Free fall in a uniform gravitational field
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Selection of the appropriate equation
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Sign conventions and units
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See every definition
- Constant acceleration equations
- Four equations link initial velocity u, final velocity v, acceleration a, displacement s and time t for constant acceleration in a straight line, and each equation omits one quantity.
- Free fall in a uniform gravitational field
- For a body falling in a uniform gravitational field without air resistance, acceleration is g, approximately 9.81 m s⁻² downwards, and a consistent positive direction must be chosen.
- Selection of the appropriate equation
- Choose the equation that matches the data and the unknown, since each equation omits one quantity.
- Sign conventions and units
- Define a positive direction consistently, assign the sign of g according to the chosen positive direction, and always check units and the sign of each vector.
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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