Tricky Topics

Question 1

Invariant Lines

Answer 1

Lines that don’t move under given transformations.

There are a few key ones given in the TB that I should remember.
(e.g. reflection in the line y = x → y = x)

…. to be continued

Question 2

Proof by Induction - Final Statement

Answer 2

• Since true for n = 1
• And true for n = k + 1
• WHEN ASSUMED true for n = k
• Thus true for all n ∈ ℤ*

Question 3

Acceleration = 0

Answer 3

• No resultant force -> Resolve to = 0
• Constant Velocity (could be 0) (N’s 1st Law)
  → Remember vice versa
• Use GCSE Speed = D/T

Question 4

Acceleration = Constant

Answer 4

SUVAT

Question 5

Acceleration = Variable

Answer 5

Differentiate given expression
(usually dx/dt)

Question 6

Vector Projection of a onto b
(Vectors in Further Mechanics)

Answer 6

(a.b / |b|^2) x b

Question 7

Forgotten Equation: Further Mech
Vectors, Impulse, e

Answer 7

-e(u . I) = v . I

Question 8

Elasticity Question Techniques

Answer 8

Work Energy Principle
- Asking for energy
- Distance
- Rest

Resolve Forces
- Acceleration

Question 10

Oblique Collisions - N’s Law of Restitution

Answer 10

v(sinβ) = eu(sinα)
v(cosβ) = u(cosα)

tanβ = e(tanα)