levo

Mathematical Requirements (Appendix C)

Choosing what to plot to find a constant

  • 2 things to know
  • All units

Overview

Recall questions on Choosing what to plot to find a constant.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

In projectile motion, what equation relates distance fallen to time, and what does the gradient of a distance versus time-squared graph represent?

Key term

For capacitor discharge, what is the equation relating ln V to time, and what does the gradient represent?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How can equations involving rates of change be solved using graphical methods?

    Model answer

    By plotting the data and finding gradients (for rates) or areas (for accumulated quantities) from the graph.

  2. 2

    In projectile motion, what equation relates distance fallen to time, and what does the gradient of a distance versus time-squared graph represent?

    Model answer

    The equation is s = ½gt². The gradient of an s against t² graph equals ½g, so g can be determined by doubling the gradient.

  3. 3

    Why is a logarithmic plot useful when analysing an exponential relationship?

    Model answer

    It converts the exponential relationship into a straight line, allowing constants to be determined from the gradient and intercept.

  4. 4

    For capacitor discharge, what is the equation relating ln V to time, and what does the gradient represent?

    Model answer

    The equation is ln V = ln V₀ − t/τ. The gradient equals −1/τ, where τ is the time constant.

  5. 5

    How can the time constant τ for capacitor discharge be obtained from a graph of ln V against time?

    Model answer

    By finding the gradient of the straight line and taking its negative reciprocal: τ = −1/gradient.

  6. 6

    If a plot of ln y against x produces a straight line, what form does the relationship between y and x take?

    Model answer

    The relationship is exponential: y = Ae^(kx), where k is the gradient and ln A is the y-intercept.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Basic Physics
Kinematics
Dynamics
Energy Concepts

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

R is the .
radiusdiametercircumference

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AF is force.
BB is magnetic flux density.
CI is current.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

A baryon means a particle built from three quarks.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Mathematical Requirements (Appendix C), on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.