Week 4#
The physics of a kangaroo strike#
The Square of Speed Has No Sympathy#
A prediction#
If a vehicle’s speed doubles, does its kinetic energy double?
Write your answer down. No calculating yet.
The equation#
E = ½ m v²
- m = mass in kilograms
- v = speed in metres per second
- E comes out in joules
speed (m/s) = speed (km/h) ÷ 3.6
Mixing up km/h and m/s is the most common way to get this wrong.
Worked calculation#
Synthetic scenario, used all lecture: a 1,500 kg vehicle.
| Speed | m/s | Kinetic energy |
|---|---|---|
| 40 km/h | 11.1 | 92.6 kJ |
E = ½ × 1,500 × (40 / 3.6)² ≈ 92,600 J
All figures are illustrative teaching inputs, not measured values.
Doubling speed#
| 40 km/h | 60 km/h | 80 km/h |
|---|---|---|
| 92.6 kJ | 208.3 kJ | 370.4 kJ |
Double the speed (40→80): quadruple the energy, not double it.
Vehicle energy is not injury severity#
- this is the vehicle’s kinetic energy — mass and speed only
- never substitute an animal’s mass into this same formula
- not a measure of energy transferred to an animal
- not a prediction of injury severity for either party
The calculator is not predicting an injury. It is explaining why speed deserves a place in the discussion.
Reaction distance#
reaction distance = speed × reaction time
Teaching assumption: 1.5 s reaction time.
| Speed | Reaction distance |
|---|---|
| 40 km/h | 16.7 m |
| 60 km/h | 25.0 m |
| 80 km/h | 33.3 m |
Scales directly with speed — nothing squared yet.
Braking distance#
braking distance = v² / (2a)
Teaching assumption: constant deceleration, a = 6.5 m/s².
| Speed | Braking distance |
|---|---|
| 40 km/h | 9.5 m |
| 60 km/h | 21.4 m |
| 80 km/h | 38.0 m |
Same squared relationship as kinetic energy.
Total stopping distance#
| 40 km/h | 60 km/h | 80 km/h |
|---|---|---|
| 26.2 m | 46.4 m | 71.3 m |
Reaction (linear) plus braking (squared) — total distance sits between the two, roughly 2.7× for double the speed.
Change one assumption#
Wet-road deceleration: a = 5.0 m/s² instead of 6.5 m/s².
| Speed | Dry (6.5 m/s²) | Wet (5.0 m/s²) |
|---|---|---|
| 40 km/h | 26.2 m | 29.0 m |
| 60 km/h | 46.4 m | 52.8 m |
| 80 km/h | 71.3 m | 82.7 m |
One changed assumption, every total shifts — check which assumption you’re relying on before trusting a number.
What the model leaves out#
- road surface
- visibility
- animal movement
- impact geometry
- vehicle deformation
- braking conditions
A simple model buys its clarity by leaving things out. This is the honest list of what it left out here.
Next week#
Every stopping distance this week starts counting only after the driver detects the animal. Next week asks what makes that detection harder in the first place — dusk, contrast, glare, fatigue.
The physics model begins after detection. Next week asks how late that starting point might be.
Professor Lindqvist accepts late assignments more readily than physics accepts late detection.