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Mathematical Requirements (Appendix C)

Mean values and periodic functions

  • 3 things to know
  • All units

Overview

Recall questions on Mean values and periodic functions.

What you need to know

Answer each one before you reveal it.

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Key term

State the kinematic relationship used to analyse a distance–time plot for a freely falling object.

Numbers

State the formula for mean velocity.

Key term

Explain why instantaneous velocity differs from mean velocity.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the formula for mean velocity.

    Model answer

    Mean velocity = Δs / Δt, where Δs is the total displacement and Δt is the total time interval.

  2. 2

    Explain why instantaneous velocity differs from mean velocity.

    Model answer

    Instantaneous velocity refers to the velocity at a specific instant, whereas mean velocity is an average calculated over a time interval.

  3. 3

    For an ideal gas at constant temperature, what is the relationship between pressure and volume, and what shape is its graph?

    Model answer

    p = k/V (an inverse relationship); the graph is a rectangular hyperbola.

  4. 4

    What approach is needed to solve 3D force problems?

    Model answer

    Visualising forces in three perpendicular directions and using geometry to find resultant magnitudes and directions.

  5. 5

    Why are 2D representations of 3D objects used in mechanics problems?

    Model answer

    To draw and interpret force diagrams when analysing forces acting in three-dimensional situations.

  6. 6

    How do you obtain the total displacement from the individual sections under a velocity–time graph?

    Model answer

    Sum the areas of all sections together.

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