AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Acceleration: initial velocity, u, in metres per second, m/s
Initial velocity, u, is the velocity of an object at the moment timing starts, measured in metres per second (m/s).
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 18 of 21
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Initial velocity, u, is the velocity of an object at the moment timing starts, measured in metres per second (m/s). Velocity is a vector: it has size and direction, so u can be positive or negative depending on the chosen positive direction. For a car starting from rest, u = 0 m/s; for a ball thrown upwards at 12 m/s, taking upwards as positive gives u = +12 m/s. In the acceleration equation a = (v − u) ÷ t, u is subtracted from final velocity v, so the change in velocity is v − u. If an object slows down, v is smaller than u and the acceleration is negative (deceleration). Always convert units to m/s before substituting: 72 km/h = 72 × 1000 ÷ 3600 = 20 m/s.
What earns the marks
- State that u is the velocity at the start of the time interval being considered, not necessarily zero.
- Recognise that u is a vector quantity, so its sign depends on the chosen positive direction.
- Use u correctly in a = (v − u) ÷ t, subtracting u from v to find the change in velocity.
- Convert speeds given in km/h or cm/s into m/s before substitution, for example 72 km/h = 20 m/s.
- Interpret a negative value of u as motion in the direction opposite to the chosen positive direction.
- Distinguish u from v: u is the initial velocity and v is the final velocity after time t.
Common mistakes and how to put them right
Assuming u is always zero.
Put it right by checking the wording; u = 0 m/s only when the object starts from rest.
Adding u and v instead of subtracting.
Put it right by using change in velocity = v − u.
Using km/h directly in the equation.
Put it right by converting to m/s first, for example divide by 3.6.
Exam tips
- Underline the starting condition in the question, such as 'from rest' or 'at 15 m/s', to fix the value of u.
- Write the equation a = (v − u) ÷ t, substitute values with units, then rearrange if needed.
- Check the sign of your answer against the motion described: slowing down should give negative acceleration.
Try the lesson
The start of the Acceleration: initial velocity, u, in metres per second, m/s lesson, made from checked teaching notes for this specification point.
Have a go first
A cyclist sets off from rest and speeds up in a straight line. What is the initial velocity u of the cyclist, in m/s?
Listen
Initial velocity, u, is the velocity of an object at the moment timing starts, measured in metres per second (m/s). Velocity is a vector: it has size and direction, so u can be positive or negative depending on the chosen positive direction. For a car starting from rest, u = 0 m/s; for a ball thrown upwards at 12 m/s, taking upwards as positive gives u = +12 m/s. In the acceleration equation a = (v − u) ÷ t, u is subtracted from final velocity v, so the change in velocity is v − u. If an object slows down, v is smaller than u and the acceleration is negative (deceleration). Always convert units to m/s before substituting: 72 km/h = 72 × 1000 ÷ 3600 = 20 m/s. A strong answer earns marks for these points. State that u is the velocity at the start of the time interval being considered, not necessarily zero. Recognise that u is a vector quantity, so its sign depends on the chosen positive direction. Use u correctly in a = (v − u) ÷ t, subtracting u from v to find the change in velocity. Convert speeds given in km/h or cm/s into m/s before substitution, for example 72 km/h = 20 m/s. A common slip: Assuming u is always zero. Instead, checking the wording; u = 0 m/s only when the object starts from rest. Exam tip: Underline the starting condition in the question, such as 'from rest' or 'at 15 m/s', to fix the value of u.
See it
Key words
Say what each word means before you turn the card.
Initial velocity, u
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Velocity
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Change in velocity
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Deceleration
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See every definition
- Initial velocity, u
- The velocity of an object at the moment timing starts, measured in metres per second (m/s).
- Velocity
- A vector quantity, so it has size and direction and can be positive or negative depending on the chosen positive direction.
- Change in velocity
- Found by subtracting initial velocity u from final velocity v, so it is v − u.
- Deceleration
- Occurs when an object slows down, so v is smaller than u and the acceleration is negative.
Label the diagram
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1Box 1
2Box 2
3Box 3
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