Formulae in Context: The Simulator
Foundation/Higher • Substitution with Negatives, Decimals & Fractions
🎮 The Physics Engine
v = u + at
Final Velocity = Initial Velocity + Acceleration × Time
Live Calculation:
v = 10 + (2 × 5)
v = 10 + 10.0
v = 20.0 m/s
💡 The Logic Track
The Negative Bucket Rule
When substituting a negative number, ALWAYS put it in brackets (the "bucket"). This protects it from confusion.
(-5)² = (-5) × (-5) = 25 ✓
-5² = -(5 × 5) = -25 ✗
The Invisible Multiply
Letters touching numbers or other letters means multiply. "2as" means 2 × a × s.
If a = 3, s = 4:
2as = 2 × 3 × 4 = 24
BIDMAS Priority
In v² = u² + 2as, you MUST square u before adding 2as.
If u = 5, a = 2, s = 10:
v² = 5² + 2(2)(10)
v² = 25 + 40 = 65
v = √65 ≈ 8.06 m/s
Notice How the Formula Updates
As you drag the sliders, watch the calculation change. The formula structure stays the same, but the numbers substitute in.
🧮 The Dynamic Solver
Example 1: Displacement Formula
s = ut + ½at²
Given: u = 0, t = 5, a = 9.8
Step 1: ut = 0 × 5 = 0
Step 2: t² = 5² = 25
Step 3: ½ × 9.8 × 25 = 122.5
s = 122.5 m
Example 2: With Current Values
s = ut + ½at²
Your values: u = 10, t = 5, a = 2
Step 1: ut = 10 × 5 = 50
Step 2: t² = 5² = 25
Step 3: ½ × 2 × 25 = 25.0
Step 4: 50 + 25.0
s = 75.0 m
🎯 Mark Scheme Tip
Edexcel examiners award method marks for showing substitution clearly. Even if your final answer is wrong, you get marks for showing "u = 10, a = 2, t = 5" substituted into the formula correctly.
Bridge Strategy Progress
Phase 1: The Anchor
Simple substitution with positive integers (v = u + at with u=10, a=2, t=5)
Phase 2: The Twist
Negative values, decimals, and bracket priorities (temperature with fractions)
Phase 3: The Killer
Multi-step SUVAT equations with v² = u² + 2as requiring square root extraction
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