---
title: "Kinetic Energy and Road Safety"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 66
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety
---

# Chapter 66 — Kinetic Energy and Road Safety

Since the wind-up toys of your childhood, [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) has been a story of stores and forms — vivid, useful, and unnumbered. The wait ends now. Motion’s [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) gets its formula, [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) gets its [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring), and the arithmetic turns out to govern a matter of life and death: why a car at double [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) is four times harder to stop, and what a single second of inattention costs in [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units).

## 66.1 The energy of motion

**Definition 66.1 (The joule).**

[Energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) — every form of it — is measured in *joules* ($\mathrm{J}$), honoring the experimenter who proved [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) itself a form of [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy). Anchors: lifting this book from floor to shelf spends a few joules; a beating heart, about one joule per beat; a chocolate bar stores a million joules of food [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy).

**Proposition 66.2 (Kinetic energy).**

A body of [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) $m$ (in $\mathrm{kg}$) moving at [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) $v$ (in $\mathrm{m}/\mathrm{s}$) carries, by virtue of its motion, the *kinetic energy*

$$
E_k = \frac{1}{2} \times m \times v^2 ,
$$

in [joules](#def-g9-kinetic-energy-safety-joule). Two dials, unequal powers: doubling the [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) doubles $E_k$ — but doubling the *[speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula)* *quadruples* it, for the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) enters squared. [Speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) is the dangerous dial.

**Example 66.3 (First computations).**

A $0.45\,\mathrm{kg}$ football at $20\,\mathrm{m}/\mathrm{s}$: $E_k = 0.5 \times
0.45 \times 20^2 = 90\,\mathrm{J}$. A $60\,\mathrm{kg}$ sprinter at $10\,\mathrm{m}/\mathrm{s}$: $0.5 \times 60 \times 100 = 3000\,\mathrm{J}$. A $1000\,\mathrm{kg}$ car at $50\,\mathrm{km}/\mathrm{h}$ — convert first: $50 \div 3.6 \approx 13.9\,\mathrm{m}/\mathrm{s}$ — $E_k = 0.5 \times
1000 \times 13.9^2 \approx 9.7 \times 10^{4}\,\mathrm{J}$: nearly a hundred thousand [joules](#def-g9-kinetic-energy-safety-joule). The same car at $100\,\mathrm{km}/\mathrm{h}$: four times as much — $3.9 \times 10^{5}\,\mathrm{J}$. The formula’s warning, in numbers.

![A one-tonne car’s kinetic energy against speed: not a line but a parabola — the square in the formula, drawn. Double the speed, quadruple the energy to be gotten rid of.](https://one-course.com/images/onecourse/chapters/physics-1/g9-kinetic-energy-safety/fig-911dfd721609.svg)

*A one-tonne car’s [kinetic energy](#prop-g9-kinetic-energy-safety-formula) against [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula): not a line but a parabola — the square in the formula, drawn. Double the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), quadruple the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) to be gotten rid of.*

**Example 66.4 (Where braking sends it).**

To stop, a car must hand its entire $E_k$ to something — [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) is passed on, never erased, as the chains of your childhood insisted. The brakes’ grip converts it to [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat): discs glow amber after mountain descents, and the smell of hot brakes *is* [kinetic energy](#prop-g9-kinetic-energy-safety-formula) retiring. In a crash the handover is violent and instantaneous — into crumpled steel. Every road-safety number below is this bookkeeping: the bigger the $E_k$, the longer, or uglier, its retirement.

![Where the kinetic energy went: the brakes and the road turned it into warmth, and the tires signed the receipt.](https://one-course.com/images/onecourse/chapters/physics-1/g9-kinetic-energy-safety/img-a7368d825e7e.jpg)

*Where the [kinetic energy](#prop-g9-kinetic-energy-safety-formula) went: the brakes and the road turned it into warmth, and the tires signed the receipt.*

## 66.2 The stopping distance

**Proposition 66.5 (Stopping = thinking + braking).**

A driver who spots danger stops only after two stretches of road:

1. the *reaction distance* : the road covered while the brain notices and the foot moves — about one full second at unchanged [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) , so this stretch grows *in proportion* to $v$ ;
2. the *braking distance* : the road the brakes need to retire the [kinetic energy](#prop-g9-kinetic-energy-safety-formula) — and since $E_k$ carries $v^2$ , this stretch grows with the *square* of the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) : double [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) , fourfold braking road.

Their sum, the *stopping distance*, is the number that meets the child chasing the ball.

**Example 66.6 (The table every driver should own).**

Dry road, alert driver (one-second reaction; good brakes):

| [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) | reaction | braking | stopping |
| --- | --- | --- | --- |
| $50\,\mathrm{km}/\mathrm{h}$ | $14\,\mathrm{m}$ | $13\,\mathrm{m}$ | $27\,\mathrm{m}$ |
| $90\,\mathrm{km}/\mathrm{h}$ | $25\,\mathrm{m}$ | $40\,\mathrm{m}$ | $65\,\mathrm{m}$ |
| $130\,\mathrm{km}/\mathrm{h}$ | $36\,\mathrm{m}$ | $85\,\mathrm{m}$ | $121\,\mathrm{m}$ |

Read it twice. At city [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), a bus-length and a half; at highway [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), a full running track and a fifth. And the proportions confirm the two laws: reaction grows like $v$, braking like $v^2$ — at high [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), braking devours the total.

**Method 66.7 (Estimating a stopping distance).**

1. convert the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) to $\mathrm{m}/\mathrm{s}$ (divide $\mathrm{km}/\mathrm{h}$ by $3.6$ );
2. [reaction distance](#prop-g9-kinetic-energy-safety-stopping) : one second’s travel — the $\mathrm{m}/\mathrm{s}$ number itself, in [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) ;
3. [braking distance](#prop-g9-kinetic-energy-safety-stopping) : scale a known anchor by the square — from $13\,\mathrm{m}$ at $50\,\mathrm{km}/\mathrm{h}$ , multiply by $(v/50)^2$ ;
4. add, and compare with what the road ahead actually offers.

Wet roads double the braking share; tired or distracted drivers stretch the reaction second toward two — rerun the sum with the honest inputs.

**Example 66.8 (The price of a glance).**

A two-second glance at a phone at $90\,\mathrm{km}/\mathrm{h}$: the car covers $2 \times 25 = 50\,\mathrm{m}$ — half a football pitch — driven blind, before any reaction second even begins. At city [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) the same glance blindly spends $28\,\mathrm{m}$: past the crossing, past the school gate. The most dangerous component of the car is unmeasured by any formula here: the driver’s attention.

**Remark 66.9 (Belts, bags and helmets).**

In a collision the car stops in a [metre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of crumpling — but an unbelted passenger continues at full [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) (the quiet sentence of last chapter, grimly applied) until stopped by whatever comes: dashboard, windscreen, road. Seat belts and airbags stop the body over a longer distance and time, retiring its [kinetic energy](#prop-g9-kinetic-energy-safety-formula) gently instead of all at once; the cyclist’s helmet does the same for the skull’s irreplaceable contents, its crushable foam buying [centimetres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of gentle stopping. None of them reduce your $E_k$ by a [joule](#def-g9-kinetic-energy-safety-joule) — they civilize its retirement.

## 66.3 Exercises

**Exercise 66.1 ★.**

Give the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) and two of its anchors, and write the [kinetic energy](#prop-g9-kinetic-energy-safety-formula) formula with its [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring).

**Solution of Exercise 66.1.**

The [joule](#def-g9-kinetic-energy-safety-joule) ($\mathrm{J}$): a few [joules](#def-g9-kinetic-energy-safety-joule) lift this book to its shelf; the heart spends about one per beat. $E_k = \frac12 m
v^2$ — $m$ in [kilograms](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-units), $v$ in [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) per second, $E_k$ in [joules](#def-g9-kinetic-energy-safety-joule).

**Exercise 66.2 ★.**

Compute $E_k$: a $2\,\mathrm{kg}$ hare at $10\,\mathrm{m}/\mathrm{s}$; an $80\,\mathrm{kg}$ rugby player at $5\,\mathrm{m}/\mathrm{s}$.

**Solution of Exercise 66.2.**

Hare: $0.5 \times 2 \times 100 = 100\,\mathrm{J}$. Player: $0.5
\times 80 \times 25 = 1000\,\mathrm{J}$.

**Exercise 66.3 ★.**

Which raises a car’s $E_k$ more: adding half its [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) in cargo, or raising its [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) by half? Show both factors.

**Solution of Exercise 66.3.**

Half more [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass): factor $1.5$. Half more [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula): factor $1.5^2
= 2.25$. The [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) dial wins — it always does, wearing the square.

**Exercise 66.4 ★.**

Name the two stretches of the stopping distance and their growth laws — one proportional, one squared.

**Solution of Exercise 66.4.**

[Reaction distance](#prop-g9-kinetic-energy-safety-stopping) — one second’s travel, growing in proportion to $v$; [braking distance](#prop-g9-kinetic-energy-safety-stopping) — the retirement of $E_k$, growing with $v^2$.

**Exercise 66.5 ★.**

From the driver’s table: what fraction of the stopping distance is braking at $50\,\mathrm{km}/\mathrm{h}$ — and at $130\,\mathrm{km}/\mathrm{h}$? What changed?

**Solution of Exercise 66.5.**

At $50\,\mathrm{km}/\mathrm{h}$: $13$ of $27\,\mathrm{m}$ — about half. At $130\,\mathrm{km}/\mathrm{h}$: $85$ of $121\,\mathrm{m}$ — some seventy percent. The squared component outgrows the proportional one: at [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), braking devours the total.

**Exercise 66.6 ★.**

Where does a braking car’s [kinetic energy](#prop-g9-kinetic-energy-safety-formula) go? Cite the smell and the glow — and the childhood law that forbids it simply vanishing.

**Solution of Exercise 66.6.**

Into [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) at the brake discs — the amber glow after mountain descents, the hot-brake smell. [Energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) is passed on, never erased: the chain proposition of the childhood [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) chapter, still in command.

**Exercise 66.7 ★.**

Compute the [reaction distance](#prop-g9-kinetic-energy-safety-stopping) at $36\,\mathrm{km}/\mathrm{h}$, $72\,\mathrm{km}/\mathrm{h}$ and $108\,\mathrm{km}/\mathrm{h}$ (one alert second). What simple pattern do the answers march to?

**Solution of Exercise 66.7.**

$36 \div 3.6 = 10\,\mathrm{m}$; then $20\,\mathrm{m}$; then $30\,\mathrm{m}$ — marching in proportion to the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), as a one-second stretch must.

**Exercise 66.8 ★.**

Why does a seat belt not reduce your [kinetic energy](#prop-g9-kinetic-energy-safety-formula) — and what does it civilize instead?

**Solution of Exercise 66.8.**

Your $E_k$ is fixed by your [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) and the car’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) — no strap changes it. The belt civilizes the *retirement*: stopping the body over a longer distance and time, gently, instead of against the dashboard, all at once.

**Exercise 66.9 ★★.**

A scooter’s [braking distance](#prop-g9-kinetic-energy-safety-stopping) is $8\,\mathrm{m}$ at $30\,\mathrm{km}/\mathrm{h}$. Estimate it at $60\,\mathrm{km}/\mathrm{h}$ and at $90\,\mathrm{km}/\mathrm{h}$ — and state the law you scaled by.

**Solution of Exercise 66.9.**

Braking scales with the square of [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula): at $60\,\mathrm{km}/\mathrm{h}$ (double), $8 \times 4 = 32\,\mathrm{m}$; at $90\,\mathrm{km}/\mathrm{h}$ (triple), $8 \times 9 = 72\,\mathrm{m}$.

**Exercise 66.10 ★★.**

Town councils lower school-zone limits from $50\,$ to $30\,\mathrm{km}/\mathrm{h}$. Compare the two stopping distances (anchor: $13\,\mathrm{m}$ of braking at $50$; one-second reaction) — and the two kinetic energies. Which comparison do you find more persuasive on a poster?

**Solution of Exercise 66.10.**

At $30\,\mathrm{km}/\mathrm{h}$: reaction $\approx 8.3\,\mathrm{m}$, braking $13 \times (30/50)^2 \approx 4.7\,\mathrm{m}$ — stopping in about $13\,\mathrm{m}$, against $27\,\mathrm{m}$ at fifty: less than half the road. Energies: $(30/50)^2 = 0.36$ — barely a third of the crash [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy). Both persuade; the poster-ready line is usually the road one — “at 30 you stop before the child; at 50 you reach them still moving”.

**Exercise 66.11 ★★.**

Rain doubles [braking distances](#prop-g9-kinetic-energy-safety-stopping). Rebuild the driver’s table’s stopping column for wet roads at $50$ and $90\,\mathrm{km}/\mathrm{h}$ — which component did you double, and which not, and why?

**Solution of Exercise 66.11.**

Double only the braking share — rain lengthens the retirement, not the brain: at $50\,\mathrm{km}/\mathrm{h}$, $14 + 26 =
40\,\mathrm{m}$; at $90\,\mathrm{km}/\mathrm{h}$, $25 + 80 = 105\,\mathrm{m}$. The reaction second is dry and wet alike.

**Exercise 66.12 ★★★.**

A truck of $20\,000\,\mathrm{kg}$ rolls at $90\,\mathrm{km}/\mathrm{h}$. Compute its $E_k$ in scientific notation; find the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) at which a $1000\,\mathrm{kg}$ car would match that [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) (set the two formulas equal — the algebra is yours this year); and conclude why runaway-truck escape ramps exist on mountain roads while no such ramps serve cars.

**Solution of Exercise 66.12.**

Truck: $v = 25$ $\mathrm{m}/\mathrm{s}$; $E_k = 0.5 \times 20000 \times
625 = 6.25 \times 10^{6}\,\mathrm{J}$. Matching car: $0.5 \times 1000 \times
v^2 = 6.25 \times 10^{6}$ gives $v^2 = 12500$, $v \approx
112\,\mathrm{m}/\mathrm{s} \approx 400\,\mathrm{km}/\mathrm{h}$ — no road car approaches it. A truck at highway [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) carries racing-car energies with lorry brakes: when they overheat and fail on a long descent, only a gravel ramp can retire megajoules safely. Cars never need one; their energies die in ordinary brakes.

## 66.4 Problem: The Safety Campaign

**Problem 66.1.**

Weekend problem — the class designs the town’s road-safety campaign; posters checked by formula; the mayor’s difficult questions

The town commissions a campaign, on one condition: every number on every poster must survive a physics audit. The class calculates. (Anchors: reaction one second; braking $13\,\mathrm{m}$ at $50\,\mathrm{km}/\mathrm{h}$, scaling by the square; car [mass](https://one-course.com/books/physics/1/en/chapter/20-measuring-mass#def-g3-measuring-mass-mass) $1000\,\mathrm{kg}$.)

**Part I — Poster one: “50 not 60”.**

1. Compute both [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) in $\mathrm{m}/\mathrm{s}$ (one decimal).
2. [Reaction distances](#prop-g9-kinetic-energy-safety-stopping) at both [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) ?
3. [Braking distances](#prop-g9-kinetic-energy-safety-stopping) at both (scale the anchor)?
4. The poster’s headline: “Ten more [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) of [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) , — how many more [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of stopping?” Fill in the number.

**Part II — Poster two: “The wall of [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula)”.** The design shows crash energies as fall heights: a crash at [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) $v$ “equals” falling from the height where the same [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) would be gained.

5. Compute the car’s $E_k$ at $50\,\mathrm{km}/\mathrm{h}$ (from Part I) and at $90\,\mathrm{km}/\mathrm{h}$ .
6. The artists need heights: falling from $1\,\mathrm{m}$ gains about $9.8\,\mathrm{kJ}$ for this car ( $m g h$ — next chapter’s other formula, borrowed early). To what fall heights do the two crash energies correspond? (Divide; round to the [metre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) .)
7. Which everyday buildings match those heights? Draft the poster’s line.
8. The mayor objects: “Nobody drives into walls; cars crumple, belts catch.” Defend the poster’s physics while conceding his point — what do crumple zones and belts change, and what number do they not change?

**Part III — Poster three: “One second”.**

9. At $90\,\mathrm{km}/\mathrm{h}$ , how many [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) does one distracted second cost before any braking? And a two-second phone glance?
10. The tired-driver variant: reaction stretched to two seconds. Recompute the full stopping distance at $90\,\mathrm{km}/\mathrm{h}$ and compare with the alert driver’s $65\,\mathrm{m}$ .
11. A skeptical councillor: “Surely a second matters little beside those big braking numbers.” At which [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) is he most wrong — low or high? (Compare the two components’ growth laws.)
12. Sign off the campaign: three poster-bottom lines, one per poster, each carrying its formula in plain words.

**Solution of Problem 66.1.**

**1.** $50 \div 3.6 = 13.9\,\mathrm{m}/\mathrm{s}$; $60 \div 3.6 =
16.7\,\mathrm{m}/\mathrm{s}$. **2.** $13.9\,\mathrm{m}$ and $16.7\,\mathrm{m}$. **3.** $13\,\mathrm{m}$; at sixty, $13 \times (60/50)^2 =
13 \times 1.44 \approx 18.7\,\mathrm{m}$. **4.** Stopping: $26.9$ against $35.4\,\mathrm{m}$ — the poster’s blank: about *eight and a half [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units)* more, two car-lengths past where the fifty-driver has stopped. **5.** At fifty: about $97\,\mathrm{kJ}$. At ninety ($v =
25\,\mathrm{m}/\mathrm{s}$): $0.5 \times 1000 \times 625 =
312\,\mathrm{kJ}$. **6.** $97 \div 9.8 \approx 10\,\mathrm{m}$; $312 \div 9.8
\approx 32\,\mathrm{m}$. **7.** Ten [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units): a three-storey house; thirty-two: a ten-storey block. Draft: “A crash at 50 is a fall from the third floor. At 90, from the tenth. Choose your window.” **8.** The heights honestly [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) that must be retired — that number no engineering changes. Crumple zones and belts change the retirement’s *manner*: [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of gentle stopping instead of [centimetres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of cruel one — which is why the fall analogy overstates injury in a modern car, and why the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) it depicts is real all the same. **9.** $25\,\mathrm{m}$ blind per second; a two-second glance, $50\,\mathrm{m}$ — half a pitch before the reaction second even starts. **10.** $65 + 25 = 90\,\mathrm{m}$ — the tired driver adds a bus-length and a half to the alert driver’s total. **11.** Most wrong at *low* [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula): there the squared braking share is small and the reaction stretch is most of the stopping distance — in town, the second *is* the danger. (At high [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) braking dominates — but $25\,\mathrm{m}$ per second is no trifle there either.) **12.** For example: “Ten more of [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), ten more [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of stopping — [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) enters twice, once squared. A crash is a fall: [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) grows with the square of [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula). One second of glance is twenty-five [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of blindness — attention is the shortest [braking distance](#prop-g9-kinetic-energy-safety-stopping) of all.”