Week 4: The physics of a kangaroo strike

Why a modest change in speed produces a disproportionate change in stopping distance and available kinetic energy — and what a simplified model can and can't tell you about that.

15 March 2027

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The Square of Speed Has No Sympathy.

Week 3 asked which road collects the most recorded collisions, and how much that answer depends on traffic and reporting. This week asks a different question entirely: once a collision is already happening, what does speed actually do to it? Collision frequency and collision severity are separate questions, with separate mathematics behind them — this lecture is about the second one.

A prediction, before the formula#

If a vehicle’s speed doubles, does its kinetic energy double? Write down an answer before reading further. Most people’s instinct says yes — twice the speed, twice the energy, a straightforward trade. The actual relationship is worse than that, in a way that matters for exactly the timetable-based thinking (“I’ll just go a little faster to make up the time”) this lecture exists to interrupt. The square of speed has no sympathy for your timetable.

Kinetic energy: the formula and the units#

The kinetic energy of a moving object is:

E = ½ m v²

where m is mass in kilograms, v is speed in metres per second, and E comes out in joules. Speed in the formula must be in metres per second, not kilometres per hour — mixing units is the single most common way to get this calculation wrong, so converting first is worth doing carefully:

speed in m/s = speed in km/h ÷ 3.6

This week uses one consistent, clearly synthetic teaching scenario throughout: a 1,500 kg vehicle, at 40, 60 and 80 km/h. Treat these as illustrative inputs chosen to make the mathematics easy to follow, not measured values, a safe driving speed, or a claim about any real vehicle.

At 40 km/h, a 1,500 kg vehicle’s kinetic energy is:

E = ½ × 1,500 × (40 / 3.6)² ≈ 92,600 J (92.6 kJ)

Doubling speed, quadrupling energy#

Now the same calculation at 80 km/h — exactly double 40 km/h:

Going from 40 to 80 km/h doubles the speed and quadruples the kinetic energy — 370.4 kJ is four times 92.6 kJ, not two. That’s what squaring a doubled number does: 2² = 4. Going from 40 to 60 km/h — a 50% increase in speed — produces a 125% increase in energy (208.3 kJ is 2.25 times 92.6 kJ, and 1.5² = 2.25). A modest change in speed buys a disproportionate change in the energy available in a collision, for exactly the same vehicle and the same driver.

This is the vehicle’s own kinetic energy — a property of its mass and speed, nothing else. It is not a measure of the energy transferred to an animal in a collision, and it is not a prediction of injury severity for either party. Those depend on impact geometry, vehicle deformation, contact area, and how the energy is actually transferred in the fraction of a second the collision takes — none of which this formula touches. Substituting an animal’s mass into this same equation would not correct for that; it would just calculate the kinetic energy of a different, hypothetical moving object, not the energy involved in an impact between two of them. This week keeps the calculation to what it can honestly claim: the vehicle’s own energy, as a function of the driver’s speed choice.

Reaction distance: the part before braking starts#

Before any braking happens at all, the vehicle keeps travelling at its original speed for the length of time it takes the driver to notice a hazard and begin braking. That distance is:

reaction distance = speed × reaction time

This week uses a stated teaching assumption of 1.5 seconds reaction time — a commonly used illustrative figure for an alert driver, not a measured value for any real driver or this unit’s dataset.

Reaction distance scales directly with speed — 33.3 m is exactly twice 16.7 m, because reaction time here is held constant and distance is just speed multiplied by a fixed number.

Braking distance: an idealised model#

Once the brakes are applied, an idealised model assumes the vehicle decelerates at a constant rate until it stops:

braking distance = v² / (2a)

where a is the (constant) deceleration in metres per second squared. This week uses a stated teaching assumption of a = 6.5 m/s² — a plausible, illustrative figure for braking on a sealed rural road, not a rating for any specific vehicle, tyre, or road surface.

Braking distance depends on the square of speed, the same way kinetic energy does — doubling speed from 40 to 80 km/h roughly quadruples the braking-distance component (9.5 m to 38.0 m), even though the driver reacts in exactly the same amount of time in both cases.

Total stopping distance#

Add the two components together:

total stopping distance = reaction distance + braking distance

Total stopping distance doesn’t double or quadruple in exact step with speed — it sits between the two, because reaction distance scales linearly with speed while braking distance scales with its square. Going from 40 to 80 km/h roughly 2.7 times the total stopping distance, for double the speed. Whatever the exact multiplier, the direction is the same one kinetic energy pointed in: speed costs you more distance and more energy than instinct suggests.

What this model leaves out#

Every number above comes from a deliberately simple model, and simple models buy their clarity by leaving things out. Treat this as a genuine limitations list, not a footnote:

• road surface — wet, gravel or icy surfaces reduce achievable deceleration well below this week’s constant figure;
• visibility — everything above assumes the driver notices the hazard at the moment reaction time starts counting, which visibility conditions (this unit’s week 5 topic) directly affect;
• animal movement — a kangaroo is not a fixed obstacle; it can move toward, away from, or across the vehicle’s path during the exact window these calculations describe;
• impact geometry — where and at what angle a collision occurs changes how energy transfers, independent of the vehicle’s total kinetic energy;
• vehicle deformation — modern vehicles are built to deform and absorb energy in a crash, which changes how much energy reaches an occupant or, in this context, an animal, compared with a perfectly rigid object;
• braking conditions — tyre condition, load, and the vehicle’s braking system all affect the real achievable deceleration, which this week holds constant by assumption.

The calculator is not predicting an injury. It is explaining why speed deserves a place in the discussion — a place the model can justify, without the model claiming to settle anything past that.

Where this goes next#

Every distance calculated this week starts counting only after the driver has detected the animal. Reaction time is a fixed input here; next week treats it as the actual subject, asking what makes detection at dusk harder in the first place — which is the question that determines whether any of this week’s stopping distances get a chance to matter at all. 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.

Reading#

Khorasani-Zavareh, D., Bigdeli, M., Saadat, S., & Mohammadi, R. (2015). “Kinetic energy management in road traffic injury prevention: a call for action”, Journal of Injury and Violence Research, 7(1), 36–37. A short, plain statement of the same physics this lecture works through — kinetic energy scaling with the square of speed, and why that makes speed management disproportionately effective compared with other variables.