Recognition Engine

Purpose

The fastest way to solve a problem is not to remember more formulas. It is to recognize the type of motion correctly.

This section acts as your Exam Decision System.

Recognition Process

Read the Question
↓
Identify the Trigger
↓
Select the Toolkit
↓
Choose the Formula

Master Recognition Tree

QUESTION APPEARS
↓
Is Acceleration Constant?
↓
YES → UAM Toolkit

NO → Calculus / Graphs / Variable Acceleration

Recognition Engine 1

Constant Acceleration?

Uniform acceleration
Constant acceleration
Constant retardation
Free fall under gravity
Velocity changes equally in equal intervals
Acceleration given as a fixed number

Examples:

a = 2 m/s²
a = -5 m/s²
g = 10 m/s²

$$v=u+at$$ $$s=ut+\frac12at^2$$ $$v^2=u^2+2as$$ $$s=\frac12(u+v)t$$

If acceleration depends on time, position or velocity such as

a = 2t
a = kx

UAM formulas are invalid.

Recognition Engine 2

Is Time Present?

After confirming UAM, ask:

Is time given?
Is time required?

$$v^2=u^2+2as$$

Typical Applications:

Stopping distance
Maximum height
Braking problems
Velocity after travelling s metres

Recognition Engine 3

Need Velocity?

$$v=u+at$$

Trigger Phrase	Immediate Action
Starts from rest	u = 0
Comes to stop	v = 0
After t seconds	Use time relation
Velocity after time	Think $v=u+at$

Recognition Engine 4

Need Displacement?

$$s=ut+\frac12at^2$$

Total distance and displacement are not always the same. Check for reversal of direction.

Recognition Engine 5

Given u, v and t?

$$s=\frac12(u+v)t$$

Useful when acceleration is absent but initial velocity, final velocity and time are known.

Recognition Engine 6

Variable Acceleration?

Examples:

a = 3t
a = kx
a = kv²

STOP

UAM INVALID

Differentiation
Integration
Chain Rule

Recognition Engine 7

Velocity Given as Function of Position?

$$a=v\frac{dv}{dx}$$

v-x Relation
↓
Chain Rule

Recognition Engine 8

Graph Question?

Graph Type
↓
Slope
↓
Area
↓
Sign
↓
Intersections

Slope = Rate of Change

Area = Accumulated Effect

Recognition Engine 9

Vertical Motion?

$$a=\pm g$$

At the highest point:

v = 0

but

a ≠ 0

Recognition Engine 10

Relative Motion?

Observer Mentioned
Train Problem
Overtaking Problem
Chase Problem

Relative Motion
↓
Individual Motion

One-Page Exam Decision Table

Trigger Seen	Immediate Tool
Constant acceleration	UAM
Time missing	$v^2=u^2+2as$
Need velocity	$v=u+at$
Need displacement	$s=ut+\frac12at^2$
Know u,v,t	$s=\frac12(u+v)t$
a=f(t)	Integration
v=f(x)	Chain Rule
Graph Given	Slope / Area
Free Fall	UAM + Gravity
Observer Mentioned	Relative Motion

Golden Exam Rule

Do not ask:

Which formula should I use?

Ask:

What type of motion is this?

Correct recognition usually leads to the correct formula.