suvat in 2D (AQA A Level Maths: Mechanics)

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Dan

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Dan

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suvat in 2D

What are the 2D/vector suvat formulae?

  • Given that acceleration is constant, four of the five suvat formulae can be used with vector
v space equals space u space plus space a t
s space equals space 1 half left parenthesis u space plus space v right parenthesis t
s space equals space u t space plus space 1 half a t squared
s space equals space v t space minus 1 half a t squared
  • The final formula begin mathsize 16px style v squared equals u squared plus 2 a s end style can not be written in vector form
    • Instead you would use this formula for each component separately (one equation using only the i components and one equation using only the j components)

How do I use the 2D/vector suvat formulae?

  • The skills involved are the same for suvat in 1D
  • Acceleration must be constant
    • If acceleration varies with time then you need to use calculus

  • All the suvat equations connect four of the five quantities
    • Knowing any three allows a fourth to be found

  • Any vector quantity used within the suvat equations (s, u, v and a) are split into i and j- components, time is a scalar and is used as normal
    • You can use one vector equation and solve that or split into two equations (one for each component) and solve them separately

Are there any additional problems with suvat when working in 2D?

  • Sometimes they won’t give you the velocity instead it could say “…a particle is travelling parallel to…”
    • This means its velocity is a scalar multiple of that vector
    • If the object is travelling parallel to the vector i then the component of velocity in the j direction must be zero and vice versa

  • The question could ask for speeds and/or distances
    • You will need to find magnitudes of relevant vectors

Worked example

2.5.1_WE_Suvat in 2D_1

(a)  Find the acceleration of the drone, giving your answer in the form begin mathsize 16px style left parenthesis a bold i plus b bold j right parenthesis space straight m space straight s to the power of negative 2 end exponent end style .

2-5-1-suvat-in-2d-example-solution-1

(b)  Find the distance of the drone from its starting point after one minute.

2-5-1-suvat-in-2d-example-solution-2

Examiner Tip

  • Don’t let the 2D aspect scare you! It works very similar to 1D suvat.
  • Always read the question carefully to see whether the answer should be a scalar or a vector.
  • Acceleration is the awkward one where we use the same word for the scalar and vector. If you are asked to find the acceleration it should be clear from the question whether it wants a scalar or a vector, if in doubt write both!

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Dan

Author: Dan

Expertise: Maths

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.