AQA · GCSE · Combined Science

    Course version: 8464 · Version from Sept 2018

    Acceleration: final velocity, v, in metres per second, m/s

    Final velocity, v, is the velocity of an object at the end of the time interval being considered, measured in metres per second (m/s).

    Checked against the AQA 8464 specification (opens in a new tab) on .

    • Point 17 of 21
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    Final velocity, v, is the velocity of an object at the end of the time interval being considered, measured in metres per second (m/s). Velocity is a vector, so v includes both speed and direction; a negative value means motion opposite to the chosen positive direction. For example, a ball thrown upwards at 15 m/s has v = 0 m/s at its highest point, then v becomes negative as it falls back. In calculations, v is the value after acceleration a has acted for time t, linked by v = u + at or v² = u² + 2as. Always identify which moment is the 'final' one, convert units if needed, and give the unit m/s with the numerical answer.

    What earns the marks

    • Define final velocity as the velocity at the end of the chosen time interval, including both magnitude and direction.
    • State the unit as metres per second, m/s, and convert values given in other units such as km/h before substituting.
    • Distinguish v from u, the initial velocity, and from average velocity, using the correct symbol in equations.
    • Apply the sign convention consistently so that a negative v indicates motion in the opposite direction to the positive direction.
    • Use v correctly in v = u + at and v² − u² = 2as, and report the answer with magnitude, unit and direction where required.

    Common mistakes and how to put them right

    • Treating v as a speed only and ignoring direction.

      Put it right: State the direction or use a sign to show velocity is a vector.

    • Confusing v with u when substituting into equations.

      Put it right: Label the start and end of the interval before choosing which value is which.

    • Giving the unit as m/s² or leaving no unit.

      Put it right: Velocity is measured in m/s; m/s² is the unit of acceleration.

    Exam tips

    • Underline the phrase 'final velocity' in the question and note the exact moment it refers to, such as 'when it hits the ground'.
    • If a value is given in km/h, convert to m/s by dividing by 3.6 before using it in an equation.
    • Include the direction or a sign in your answer when the motion reverses, and keep the same positive direction throughout the calculation.

    Try the lesson

    The start of the Acceleration: final velocity, v, in metres per second, m/s lesson, made from checked teaching notes for this specification point.

    Have a go first

    A cyclist speeds up from rest and reaches a final velocity of 8 m/s. What is the value of v for this cyclist?

    Listen

    Final velocity, v, is the velocity of an object at the end of the time interval being considered, measured in metres per second (m/s). Velocity is a vector, so v includes both speed and direction; a negative value means motion opposite to the chosen positive direction. For example, a ball thrown upwards at 15 m/s has v = 0 m/s at its highest point, then v becomes negative as it falls back. In calculations, v is the value after acceleration a has acted for time t, linked by v = u + at or v² = u² + 2as. Always identify which moment is the 'final' one, convert units if needed, and give the unit m/s with the numerical answer. A strong answer earns marks for these points. Define final velocity as the velocity at the end of the chosen time interval, including both magnitude and direction. State the unit as metres per second, m/s, and convert values given in other units such as km/h before substituting. Distinguish v from u, the initial velocity, and from average velocity, using the correct symbol in equations. Apply the sign convention consistently so that a negative v indicates motion in the opposite direction to the positive direction. A common slip: Treating v as a speed only and ignoring direction. Instead, state the direction or use a sign to show velocity is a vector. Exam tip: Underline the phrase 'final velocity' in the question and note the exact moment it refers to, such as 'when it hits the ground'.

    See it

    A flowchart running from top to bottom with six steps. The first step is to identify the final moment of the time interval. The second is to distinguish v, the final velocity, from u, the initial velocity. The third is to convert any values given in other units, such as km/h, to m/s. The fourth is to apply the sign convention consistently. The fifth is to use v in v = u + at or v² − u² = 2as. The sixth is to report the answer with magnitude, unit m/s and direction where required. Each step leads to the next.
    It shows the sequence of steps for identifying and using final velocity, v, in calculations.

    Put it in order

    Put these steps in the order they happen.

    1. 1. Convert any values given in other units, such as km/h, to m/s
    2. 2. Distinguish v (final velocity) from u (initial velocity)
    3. 3. Identify the final moment of the time interval
    4. 4. Report the answer with magnitude, unit m/s and direction where required
    5. 5. Use v in v = u + at or v² − u² = 2as
    6. 6. Apply the sign convention consistently

    Key words

    Say what each word means before you turn the card.

    Final velocity

    Try answering aloud or in your head before turning the card.

    Velocity as a vector

    Try answering aloud or in your head before turning the card.

    Units and unit conversion

    Try answering aloud or in your head before turning the card.

    Sign conventions

    Try answering aloud or in your head before turning the card.

    See every definition
    Final velocity
    The velocity of an object at the end of the time interval being considered, measured in metres per second (m/s).
    Velocity as a vector
    A quantity that includes both speed and direction, so a negative value means motion opposite to the chosen positive direction.
    Units and unit conversion
    Values given in other units such as km/h are converted before substituting, and the answer is given with the unit m/s.
    Sign conventions
    Applied consistently so that a negative value indicates motion in the opposite direction to the positive direction.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A flowchart running from top to bottom with six steps. The first step is to identify the final moment of the time interval. The second is to distinguish v, the final velocity, from u, the initial velocity. The third is to convert any values given in other units, such as km/h, to m/s. The fourth is to apply the sign convention consistently. The fifth is to use v in v = u + at or v² − u² = 2as. The sixth is to report the answer with magnitude, unit m/s and direction where required. Each step leads to the next.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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