suvat in 2D

Given that acceleration is constant, four of the five suvat formulae can be used with vector

v = u + a t

s = \frac{1}{2} (u + v) t

s = u t + \frac{1}{2} a t^{2}

s = v t - \frac{1}{2} a t^{2}

The final formula $v^{2} = u^{2} + 2 a s$ 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)

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

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

2.5.1_WE_Suvat in 2D_1

(a) Find the acceleration of the drone, giving your answer in the form $(a i + b j) m s^{- 2}$ .

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

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!

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