## Basic mechanics

Context kinematics

uses quantities/length

uses quantities/time

uses quantities/velocity

uses quantities/acceleration

### 1` `Kinematics

The derived quantities V and A are obtained as quotients of the fundamental quantities L and T.

L ÷ Tnz : V

Lnz ÷ Tnz : Vnz

V ÷ Tnz : A

Vnz ÷ Tnz : Anz

Context kinematics-example

extends kinematics

#### 1.1` `Example

We consider a point that moves on a straight line starting at time 0 from the origin. At time t1 : Tnz it has distance d1 : L from the origin, at time t2 : Tnz, t2 > t1 the distance is d2 : L.

v1 : V

v1 ⇒ d1 ÷ t1.

v2 : V

v2 ⇒ d2 ÷ t2.

a : A

a ⇒ 2 × ((v2 - v1) ÷ (t2 - t1))

a ⇒ 2 × (((d2 ÷ t2) - (d1 ÷ t1)) ÷ (t2 - t1)).

Context kinematics-nummerical-example

extends kinematics-example

t1 ⇒ 3 × s, d1 ⇒ 20 × m

t2 ⇒ 6 × s, d2 ⇒ 50 × m

v1 ⇒ 20/3 × (m ÷ s)

v2 ⇒ 25/3 × (m ÷ s)

a ⇒ 10/9 × (m ÷ s ÷ s).

Context time-dependent-kinematics

extends kinematics

includes transformed quantities/function-with-finite-difference-template

includes transformed quantities/function-with-finite-difference-template

### 2` `Time-dependent kinematics

When describing motion, quantities L, V, and A become functions of T. These time-dependent quantities are written as T→L ⊆ T→Q, T→V ⊆ T→Q, and T→A ⊆ T→Q, with each one being the time derivative of its predecessor. The sort T→Q ⊆ Q→Q covers all these time-dependent quantities.

Context dynamics

extends time-dependent-kinematics

uses quantities/mass

uses quantities/force

includes transformed quantities/function-template

### 3` `Dynamics

M × A : F

Mnz × Anz : Fnz

M × T→A : T→F

(m × f)[t] ⇒ m × f[t]

∀ m : M

∀ t : T

∀ f : T→A