Keep adding the +c and then removing it with proof at every stage e.g. v = something at t = 0

Dont need in vector form - too complex to square vectors for single maths. Use the basic formulas and use i and j for simple algebra

When integrating i and j coefficients

Make sure to add c1, c2, etc to both i and j at every stage, proving each of them into constants at each stage as per normal

r = xi + yj. What is r?

Position vector. Not the same thing as displacement. When calculating using suvat, add the displacement to the start point to get r.

Where r = xi + yj, where x and y are expressions in terms of t, can sometimes eliminate variable t to get a cartesian equation. 1. Find x and y equations 2. Rearrange easiest for t 3. Sub into the other equation 4. Simplify

Domain of x using cartesian

t can only be positive so shows what domain of x. e.g. x = t + 2, so x =< 2

e.g. Find cartesian equation for path of particle r = (t^2 - 2)i + (t+1)j

x = t^2 - 2 y = t + 1 t = y - 1 x = (y-1)^2 - 2 x = y^2 - 2y - 1

Symmetry of projectile motion

Dont assume symmetry for e.g. landing angle. DRAW DIAGRAM. If starting at a weird point, add the vector position of its start point to the displacement

'30 degrees above/below horizontal'

For v^2 suvat equation

No t, so is +- as multiple possible points can be there. Watch out for the +-

For force diagram questions

Give values if at all possible Add resistance, tension, etc if relevant - dont miss one Add acceleration value too if given

Make sure they're *end-to-end* - rearrange if needed

When resolving perpendicular/parallel to slope

Make sure to add the perpendicular and parallel components of weight or other horizontal/vertical forces to the ones already in correct directions. Also make sure arrows going correct way to be end-to-end of resultant of weight

When given the bearing something is moving at and multiple times in your answer

To remove solutions, check to make sure that at both times it's moving in the correct bearing not the opposite direction.

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Maths Y13 Mech

Maths Spring Y13

Question	Answer
When integrating	Keep adding the +c and then removing it with proof at every stage e.g. v = something at t = 0
v^2 = u^2 + 2as	Dont need in vector form - too complex to square vectors for single maths. Use the basic formulas and use i and j for simple algebra
Speed	Give magnitude
When integrating i and j coefficients	Make sure to add c1, c2, etc to both i and j at every stage, proving each of them into constants at each stage as per normal
r = xi + yj. What is r?	Position vector. Not the same thing as displacement. When calculating using suvat, add the displacement to the start point to get r.
Cartesian equations	Where r = xi + yj, where x and y are expressions in terms of t, can sometimes eliminate variable t to get a cartesian equation. 1. Find x and y equations 2. Rearrange easiest for t 3. Sub into the other equation 4. Simplify
Domain of x using cartesian	t can only be positive so shows what domain of x. e.g. x = t + 2, so x =< 2
e.g. Find cartesian equation for path of particle r = (t^2 - 2)i + (t+1)j	x = t^2 - 2 y = t + 1 t = y - 1 x = (y-1)^2 - 2 x = y^2 - 2y - 1
Range from projectile motion	The x displacement
Symmetry of projectile motion	Dont assume symmetry for e.g. landing angle. DRAW DIAGRAM. If starting at a weird point, add the vector position of its start point to the displacement
Phrasing for angle	'30 degrees above/below horizontal'
For v^2 suvat equation	No t, so is +- as multiple possible points can be there. Watch out for the +-
For force diagram questions	Give values if at all possible Add resistance, tension, etc if relevant - dont miss one Add acceleration value too if given
Resultant forces	Make sure they're end-to-end - rearrange if needed
When resolving perpendicular/parallel to slope	Make sure to add the perpendicular and parallel components of weight or other horizontal/vertical forces to the ones already in correct directions. Also make sure arrows going correct way to be end-to-end of resultant of weight
When given the bearing something is moving at and multiple times in your answer	To remove solutions, check to make sure that at both times it's moving in the correct bearing not the opposite direction.

Created by: Pyrogearos2

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