---
title: "Motion: Uniform and Varied"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 65
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/65-motion-uniform-and-varied
---

# Chapter 65 — Motion: Uniform and Varied

Two years ago you diagnosed motion by eye: evenly spaced dots, uniform; spreading dots, speeding up. This year the dots get millimetre rulings and the diagnosis gets numbers — interval by interval, [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) by [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula). And at the chapter’s end stands a quiet sentence about [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) and motion that will one day carry half of physics on its back.

## 65.1 The record of motion

**Definition 65.1 (Timed position records).**

A *timed position record* of a motion marks the moving object’s positions at equal ticks of time — video frames stepped through, a blinking strobe photograph, or the laboratory’s dot-timer stamping a paper tape pulled by the object, fifty dots a second. Between any two neighboring marks lies one tick’s worth of travel: the record turns motion into measurable segments.

**Method 65.2 (Reading a record with numbers).**

For a record with tick length $\tau$ (say $0.02\,\mathrm{s}$ for fifty a second, or a comfortable $0.1\,\mathrm{s}$ from video):

1. [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) each gap between neighboring marks with the millimetre ruler;
2. divide each gap by the tick: $v = d/\tau$ gives the (average) [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) over that little interval — in $\mathrm{m}/\mathrm{s}$ if the gaps are in [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) ;
3. lay the [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) side by side and read the story: steady numbers, [uniform motion](https://one-course.com/books/physics/1/en/chapter/40-describing-motion-trajectory-and-speed#def-g6-describing-motion-uniform) ; climbing, accelerated; sinking, decelerated;
4. quote any interval’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) as the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) “at” that moment: over so short a tick, average and instantaneous shake hands.

![Three tapes from the dot-timer, one dot per tick. This year the gaps are measured, and each one becomes a speed.](https://one-course.com/images/onecourse/chapters/physics-1/g9-uniform-varied-motion/fig-3a33ad3d576f.svg)

*Three tapes from the dot-timer, one dot per tick. This year the gaps are measured, and each one becomes a [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula).*

**Example 65.3 (A tape, worked).**

A trolley’s tape, ticks of $0.1\,\mathrm{s}$, gaps in [centimetres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units): $2.0$, $3.0$, $4.0$, $5.0$, $6.0$. [Speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), gap by gap: $0.02 \div 0.1 = 0.2\,\mathrm{m}/\mathrm{s}$, then $0.3$, $0.4$, $0.5$, $0.6\,\mathrm{m}/\mathrm{s}$. Verdict: accelerated — and beautifully regularly so: the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) grows by exactly $0.1\,\mathrm{m}/\mathrm{s}$ each tick. Motions whose [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) climbs by equal steps in equal times have a special name and a great future — *uniformly* accelerated, the signature of steady causes.

**Example 65.4 (The most famous accelerated motion).**

Drop a stone and film it: the gaps stretch tick by tick — free fall is accelerated. Measured, its [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) grows by about $9.8\,\mathrm{m}/\mathrm{s}$ in each second of falling: after one second, $9.8\,\mathrm{m}/\mathrm{s}$; after two, nearly $20\,\mathrm{m}/\mathrm{s}$. That the growth rate equals the place’s $g$ is no coincidence — it is the deepest rhyme in this year’s physics, and the High School volume builds its mechanics upon it. Note it, underline it, and let it wait.

## 65.2 Instantaneous speed, honestly

**Definition 65.5 (Instantaneous speed).**

The *instantaneous speed* of a motion at some moment is the [average speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-average) over a very short interval around that moment — so short that the motion has no room to change its pace within it. It is the speedometer’s number and the radar’s: both, in fact, [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) exactly as [Method 65.2](#met-g9-uniform-varied-motion-read) does, over ticks of a wink. (What “very short” means with full rigor is the great question the last year of high school mathematics answers — and the answer created modern science.)

**Example 65.6 (Average and instantaneous, side by side).**

A metro run between stations: [average speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-average) — total distance over total time — $35\,\mathrm{km}/\mathrm{h}$. [Instantaneous speed](#def-g9-uniform-varied-motion-instant): $0$ at both platforms, $70\,\mathrm{km}/\mathrm{h}$ mid-tunnel. In [uniform motion](https://one-course.com/books/physics/1/en/chapter/40-describing-motion-trajectory-and-speed#def-g6-describing-motion-uniform), and only there, the two notions merge into one steady number: [uniform motion](https://one-course.com/books/physics/1/en/chapter/40-describing-motion-trajectory-and-speed#def-g6-describing-motion-uniform) is precisely the motion that makes [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) a single, honest, interval-free quantity.

## 65.3 The quiet sentence

**Proposition 65.7 (Balanced forces leave motion unchanged).**

When the [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) on a body cancel each other out — or when none act at all — the body’s motion does not change: at rest it remains at rest, and moving it continues in a straight line at constant [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula). Change of motion — speeding, slowing, turning — occurs only while some *unbalanced* [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) acts. This sentence, stated here and honestly deferred, is the opening law of all mechanics; the High School volume begins with it and never lets go.

**Example 65.8 (Reading the world with the sentence).**

The puck on smooth ice glides straight and steady — [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) balanced ([weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) down, ice up), motion unchanged: no push needed to *keep* going. The braking car slows: one unbalanced [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force), the road’s grip on the tires, acting backward. The turning cyclist: unbalanced [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) sideways, supplied by the leaning tires. And the cruising airliner at steady $900\,\mathrm{km}/\mathrm{h}$: thrust balancing drag, lift balancing [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) — four [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force), perfect tie, [uniform motion](https://one-course.com/books/physics/1/en/chapter/40-describing-motion-trajectory-and-speed#def-g6-describing-motion-uniform). Stillness and cruising are, to physics, the same peaceful state.

**Remark 65.9 (Why the sentence surprises).**

Daily life seems to protest: stop pedaling and the bicycle slows — surely motion *needs* [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force)? But the slowing bicycle is not force-free: friction and [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) push backward, unbalanced, and that is exactly why the pace decays. Remove them — the ice rink, the void of space — and motion coasts forever: the space probes launched before your grandparents met are still coasting now, engines cold. Humanity needed two thousand years to see through friction’s disguise; you have the advantage of ice rinks and space probes.

## 65.4 Exercises

**Exercise 65.1 ★.**

What is a [timed position record](#def-g9-uniform-varied-motion-record)? Name two ways of making one.

**Solution of Exercise 65.1.**

Marks of the object’s positions at equal ticks of time. Two makers: stepping through video frames; the dot-timer stamping a pulled paper tape (or a strobe photograph).

**Exercise 65.2 ★.**

A tape with $0.1\,\mathrm{s}$ ticks shows gaps of $4.0\,\mathrm{cm}$, $4.0$, $4.0$, $4.0$. Diagnose the motion and give its [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) in $\mathrm{m}/\mathrm{s}$.

**Solution of Exercise 65.2.**

Equal gaps: uniform. $v = 0.04 \div 0.1 = 0.4\,\mathrm{m}/\mathrm{s}$.

**Exercise 65.3 ★.**

Another tape: gaps $1.0$, $2.5$, $4.5$, $7.0\,\mathrm{cm}$. Diagnose — and compute the first and last interval [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula).

**Solution of Exercise 65.3.**

Growing gaps: accelerated. First interval: $0.01 \div 0.1 =
0.1\,\mathrm{m}/\mathrm{s}$; last: $0.07 \div 0.1 = 0.7\,\mathrm{m}/\mathrm{s}$.

**Exercise 65.4 ★.**

Distinguish average from [instantaneous speed](#def-g9-uniform-varied-motion-instant) on a school run: which does the radar by the gate read, and which does the family’s “twenty minutes door to door” compute?

**Solution of Exercise 65.4.**

The radar reads [instantaneous speed](#def-g9-uniform-varied-motion-instant) — the pace at the gate’s instant. “Twenty minutes door to door” computes the average — total distance over total time, stops and sprints blended.

**Exercise 65.5 ★.**

In which motions do average and [instantaneous speed](#def-g9-uniform-varied-motion-instant) coincide? Why there and only there?

**Solution of Exercise 65.5.**

In [uniform motions](https://one-course.com/books/physics/1/en/chapter/40-describing-motion-trajectory-and-speed#def-g6-describing-motion-uniform): the pace never changes, so every interval — long or wink-short — returns the same number, and the two notions collapse into one.

**Exercise 65.6 ★.**

By how much does a freely falling stone’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) grow each second, and what local number does that growth equal?

**Solution of Exercise 65.6.**

By about $9.8\,\mathrm{m}/\mathrm{s}$ each second — numerically the local $g$, $9.8\,\mathrm{N}/\mathrm{kg}$: the year’s deepest rhyme.

**Exercise 65.7 ★.**

State the quiet sentence. What does it say about a body with no [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) at all — and about the cruising airliner’s four-way tie?

**Solution of Exercise 65.7.**

Balanced (or absent) [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) leave motion unchanged: rest stays rest, and steady straight motion continues. The force-free body coasts forever; the airliner’s four-way tie — thrust against drag, lift against [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) — is exactly why its $900\,\mathrm{km}/\mathrm{h}$ holds steady.

**Exercise 65.8 ★.**

“Motion needs [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) to continue.” Convict this ancient error with the coasting space probe and friction’s disguise.

**Solution of Exercise 65.8.**

The probe, force-free in the void, has coasted for decades with cold engines — motion needing no [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) to continue. The bicycle that “proves” otherwise slows under friction and [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air), unbalanced backward [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) in disguise; on ice, with the disguise thinned, it coasts far.

**Exercise 65.9 ★★.**

A tape ($0.1\,\mathrm{s}$ ticks) reads, in [centimetres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units): $6.0$, $5.0$, $4.0$, $3.0$, $2.0$. Diagnose; compute each interval [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula); and predict the tape’s future if the pattern holds.

**Solution of Exercise 65.9.**

Shrinking gaps: decelerated. [Speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula): $0.6$, $0.5$, $0.4$, $0.3$, $0.2\,\mathrm{m}/\mathrm{s}$ — falling by $0.1\,\mathrm{m}/\mathrm{s}$ per tick. If the pattern holds, two more ticks ($1.0\,\mathrm{cm}$, then nothing) bring the tape to rest.

**Exercise 65.10 ★★.**

The worked trolley gained $0.1\,\mathrm{m}/\mathrm{s}$ per tick of $0.1\,\mathrm{s}$. Express that growth per *second* — and compare the trolley’s gain with free fall’s.

**Solution of Exercise 65.10.**

$0.1\,\mathrm{m}/\mathrm{s}$ per $0.1\,\mathrm{s}$ is $1\,\mathrm{m}/\mathrm{s}$ gained per second — about a tenth of free fall’s $9.8\,\mathrm{m}/\mathrm{s}$ per second: a gentle push beside the Earth’s.

**Exercise 65.11 ★★.**

A parachutist falls faster and faster — then, canopy open, at a steady $5\,\mathrm{m}/\mathrm{s}$. Read both [phases](https://one-course.com/books/physics/1/en/chapter/51-phases-of-the-moon#def-g7-moon-phases-phases) with the quiet sentence: what is unbalanced at first, and what tie has formed by the end?

**Solution of Exercise 65.11.**

First phase: [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) outpulls the young air resistance — unbalanced downward [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force), [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) grows. Canopy open: the blossoming [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) drag rises until it ties the [weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight) exactly — balanced [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force), and the fall settles to the steady $5\,\mathrm{m}/\mathrm{s}$ the sentence promises.

**Exercise 65.12 ★★★.**

Design the full laboratory verdict on a toy car released down a ramp onto a carpet: the record to take, the numbers to compute, the expected two-act diagnosis (which act on the ramp, which on the carpet), and the force-sentence reading of each act.

**Solution of Exercise 65.12.**

Record: film the release and step frames at $0.1\,\mathrm{s}$ (or tape the car to the dot-timer); [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) gap after gap down ramp and across carpet. Numbers: interval [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), listed in order. Expected verdict: act one, growing gaps — accelerated on the ramp ([weight](https://one-course.com/books/physics/1/en/chapter/24-weight-and-mass#def-g4-weight-and-mass-weight)’s unbalanced share along the slope); act two, shrinking gaps — decelerated on the carpet (friction’s unbalanced backward [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force)). One toy, both faces of the quiet sentence.

## 65.5 Problem: The Tape Bureau

**Problem 65.1.**

Weekend problem — an afternoon at the motion-analysis bureau; four tapes, four verdicts; the inspector’s rhyme

The bureau analyzes timed records for schools, sports clubs and courts. Ticks are $0.1\,\mathrm{s}$ throughout; gaps arrive in [centimetres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units). You hold the ruler.

**Part I — Routine verdicts.**

1. Tape A (a corridor walker): $8.0$ , $8.0$ , $8.0$ , $8.0$ , $8.0$ . Verdict and [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) — in $\mathrm{m}/\mathrm{s}$ and $\mathrm{km}/\mathrm{h}$ .
2. Tape B (a sprinter’s start): $2.0$ , $4.0$ , $6.0$ , $8.0$ , $10.0$ . Verdict, first and last [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) , and the per-second growth of [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) .
3. Tape C (a rolling ball meeting sand): $10.0$ , $7.0$ , $4.5$ , $2.5$ , $1.0$ . Verdict — and the force-sentence’s account of the sand.
4. Tape D (a mystery): $5.0$ , $5.0$ , $5.0$ , $7.5$ , $10.0$ . Tell D’s two-act story, and mark the tick where something happened.

**Part II — The bureau’s physics desk.**

5. A client insists their delivery scooter “was doing $30\,\mathrm{km}/\mathrm{h}$ , officer, on average”. The radar logged $55\,\mathrm{km}/\mathrm{h}$ at the crossing. Explain to the client why both numbers can be true and which one the law reads.
6. Tape B’s sprinter gains [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) by equal steps. What single word does the bureau stamp on such motion, and what does the steadiness of the growth suggest about the pushing [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) ?
7. The corridor walker of tape A, says the force-sentence, walks under balanced [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) . Name the balance for a steady walker (what pushes, what resists).
8. A stone’s fall-tape shows interval [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) $0.98$ , $1.96$ , $2.94\,\mathrm{m}/\mathrm{s}$ . Verify the per-second growth and name the number it reproduces.

**Part III — The court case.** A skateboard rolled from a ramp across a schoolyard into a flowerbed; the caretaker blames “reckless [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula)”, the skater claims “I was slowing all along”. The yard camera yields gaps: ramp exit $12.0$, then $11.5$, $11.0$, $10.5$, $10.0$ into the flowerbed.

9. Verdict on the skater’s claim — with the interval [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) .
10. Exit [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) and flowerbed-entry [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) in $\mathrm{km}/\mathrm{h}$ : was either “reckless” beside a brisk cyclist’s $15\,\mathrm{km}/\mathrm{h}$ ?
11. The caretaker asks why the board did not simply stop on flat ground “as things naturally do”. The bureau’s answer, in one sentence of force-language.
12. Close the file with the inspector’s rhyme — two lines: what equal gaps mean, and what changing gaps demand (a cause, by the quiet sentence).

**Solution of Problem 65.1.**

**1.** Uniform; $v = 0.08 \div 0.1 = 0.8\,\mathrm{m}/\mathrm{s}
\approx 2.9\,\mathrm{km}/\mathrm{h}$ — a stroll. **2.** Accelerated: from $0.02 \div 0.1 = 0.2\,\mathrm{m}/\mathrm{s}$ to $1.0\,\mathrm{m}/\mathrm{s}$; gaining $0.2\,\mathrm{m}/\mathrm{s}$ per tick — $2\,\mathrm{m}/\mathrm{s}$ per second. **3.** Decelerated, steeply. The sand supplies a large unbalanced backward [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) — deep friction — and the [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) tumble: $1.0$, $0.7$, $0.45$, $0.25$, $0.1\,\mathrm{m}/\mathrm{s}$. **4.** Three ticks of uniform gliding at $0.5\,\mathrm{m}/\mathrm{s}$, then acceleration — gaps leaping to $7.5$ and $10.0\,\mathrm{cm}$: between ticks three and four something began to push (a slope, a shove). The event lives at the third gap’s end. **5.** Both can be true: the average blends waiting and riding over the whole trip; the radar reads the crossing’s instant. Traffic law reads the radar — limits govern [instantaneous speed](#def-g9-uniform-varied-motion-instant), and no gentle average excuses a fast instant. **6.** Uniformly accelerated. Equal speed-steps in equal times point to a steady, unchanging net push — constant cause, constant growth. **7.** The walker’s forward push from the ground on the shoes ties the backward drags of [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) and ground on the body: balanced, hence the steady $0.8\,\mathrm{m}/\mathrm{s}$. **8.** Growth: $0.98\,\mathrm{m}/\mathrm{s}$ per tick of $0.1\,\mathrm{s}$ — $9.8\,\mathrm{m}/\mathrm{s}$ per second: the local $g$, reproduced by a falling stone’s tape. **9.** The claim holds: [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) $1.2$, $1.15$, $1.10$, $1.05$, $1.0\,\mathrm{m}/\mathrm{s}$ — slowing, gently, all along. **10.** Exit $1.2 \times 3.6 = 4.3\,\mathrm{km}/\mathrm{h}$; entry $3.6\,\mathrm{km}/\mathrm{h}$ — both far below the cyclist’s benchmark: recklessness acquitted; steering, perhaps, another matter. **11.** “On flat ground nothing stops a rolling board except unbalanced backward friction — smooth yards supply little, so the board keeps most of its motion, exactly as the law of balanced [forces](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) says it must.” **12.** For example: “Equal gaps, a pace at peace — no net [force](https://one-course.com/books/physics/1/en/chapter/12-pushes-and-pulls-forces#def-g2-pushes-and-pulls-force) disturbs its lease. Changing gaps demand a cause: some unbalanced push, by the quiet clause.”