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Category: Mechanics

  • How Do I Know Which SUVAT Equation to Use.

    You probably know the SUVAT equations.
    You probably know how to substitute into them.

    But in an A level exam, with those long, messy mechanics questions, it’s very easy to sit there thinking:

    “Which SUVAT equation do I use here?”

    And then the guessing starts.

    You’re not bad at maths. There is a simple way to deal with it.

    The mistake most students make

    Most students look at the list of equations and think:

    “Which one looks right? – Vibes it…”

    You don’t start with equations.
    You start with the information the question gives you.

    The method that actually works

    First, write out the letters:

    S (Displacement)
    U (Initial Velocity)
    V (Final Velocity)
    A (Acceleration)
    T (Time)

    Now go through the question and write down which letters you know the value for.

    For example:

    • if it says “starts from rest”, then u = 0
    • if it takes 5 seconds, then t is known
    • if it is accelerating, then a is known

    List the letters you have.

    Finally, don’t forget the letter you are looking for. For example, if we are looking for the final velocity, we also list v.

    The Five SUVAT Equations

    1. v = u + at
    2. s = ut + ½at²
    3. s = vt − ½at²
    4. v² = u² + 2as
    5. s = (u + v) / 2 × t

    We can now look at which equation contains all 4 letters we listed.

    v = u + at

    The first equation contains all our letters, so we pick this one!

    That’s it

    That’s the whole method.

    Write the letters.
    List what you know.
    Include what you’re finding.
    Pick the equation that contains all four.

    Once you do it this way, SUVAT stops feeling random and starts feeling controlled.

    And that’s exactly what you want in an exam.

  • What Does “Comment On The Validity of a Model” Mean in A Level Mechanics

    What Does “Comment On The Validity of a Model” Mean in A Level Mechanics

    Why negative heights appear, and why they aren’t calculation errors

    You substitute the values.
    The maths works.

    Then the answer says the golf ball is 48 metres below the ground.

    That’s usually when students stop and think:
    “Why am I getting a negative height?”

    Illustration showing a mathematical model predicting a golf ball below ground, representing negative height in A-Level Mechanics

    In exam questions, this often appears alongside a line like:

    Comment on the validity of the model.

    It feels like an algebra mistake, but it isn’t! The maths is doing exactly what it should. The problem is something else.

    So What Is Going On?

    The equation looks flawless.
    The numbers come out neatly.

    So under pressure, it’s very natural to assume:
    If I’m given a value of xx, I’m meant to substitute it.

    That instinct is usually correct, however…

    A mathematical model doesn’t know anything about golf balls, gravity, or the ground. It will happily keep producing outputs long after the real situation it represents has stopped making sense.

    The mistake isn’t using the model.
    The mistake is forgetting when it stops describing reality.

    That’s exactly what examiners are testing when they ask about validity.

    What This Looks Like In Practice

    Suppose the height of a golf ball is modelled by

    h=0.36x−0.003x2h = 0.36x – 0.003x^2

    where:

    • hh is the height above the ground (in metres)
    • xx is the horizontal distance travelled (in metres)

    This is an upside-down quadratic. That already tells us something important: the ball goes up, reaches a maximum height, then comes back down.

    To find when the ball hits the ground, we set the height equal to zero:

    0=0.36x−0.003x20 = 0.36x – 0.003x^2

    Factorising:0=x(0.36−0.003x)0 = x(0.36 – 0.003x)

    This gives two solutions:

    • x=0x = 0
    • x=120x = 120

    These aren’t just numbers. They have meaning.

    • x=0x = 0 the ball starts on the ground
    • x=120x = 120 the ball lands back on the ground

    So the model describes the flight of the ball only between 0 and 120 metres.

    That interval matters more than the formula itself.

    A Worked Example (Where Things Usually Go Wrong)

    Now suppose you’re asked:

    Use the model to predict the height of the golf ball when it is 200 metres from the golfer.

    If you substitute x=200x = 200

    h=0.36(200)−0.003(200)2=72−120=−48h = 0.36(200) – 0.003(200)^2 = 72 – 120 = -48

    Mathematically? Perfectly correct.
    Physically? Impossible.

    This is the point examiners care about.

    The model is now predicting a height below the ground, which tells you something crucial:
    the model is being used outside its valid range.

    The ball has already landed at 120 metres. Beyond that point, the original situation “a golf ball in flight” no longer exists.

    The negative height isn’t an error.
    It’s a warning sign.

    The Key Takeaway

    1. A model will always give an output, even when it no longer represents reality.
    2. Solving h=0h = 0 tells you where the model starts and stops being valid, not just where the maths works.
    3. Values outside that range can be algebraically correct while being physically meaningless.

    So when you’re asked to comment on validity:

    Does this result still make sense in the real situation being modelled?

    If This Still Feels Hard…

    If this topic feels more confusing than expected, it’s usually because of gaps in:

    • Interpreting solutions in context (what answers mean, not just what they are)
    • Understanding quadratics as shapes, not just formulas
    • Linking graphs to real-world behaviour
    • Knowing when substitution is appropriate, and when it isn’t

    Once you tighten up on these, applying them becomes easier.

    Final Thought

    Mathematical models are powerful precisely because they simplify reality, but that simplification always comes with limits.

    When an answer feels “wrong”, it’s often because the maths has quietly gone past the point where the real situation still applies. Learning to spot that moment is what separates calculation from understanding.

    And once you see it, questions like these stop feeling weird and start making sense.