SOLID STATE PRESS
← Back to catalog
1D Kinematics: Motion in a Straight Line cover
Coming soon
Coming soon to Amazon
This title is in our publishing queue.
Browse available titles
Physics

1D Kinematics: Motion in a Straight Line

A High School & College Primer on Position, Velocity, and Acceleration

Physics class just assigned kinematics, the exam is in a week, and the textbook reads like a legal document. Or maybe your student is staring at a velocity-time graph with no idea what any of it means. This guide is the shortcut.

**TLDR: 1D Kinematics** covers everything a high school or first-year college student needs to understand motion along a straight line — from setting up a coordinate axis and defining displacement all the way through the four constant-acceleration equations and free-fall problems. Six focused sections walk you through position, velocity, and speed (and why they're not the same thing), how to read x-t and v-t graphs without guessing, and why "negative acceleration" doesn't always mean an object is slowing down. The final section is a compact problem-solving playbook that targets the specific mistakes that cost students the most points on tests.

This is an ap physics 1 kinematics quick review guide in the truest sense: no filler chapters, no padding, no re-teaching things you already know. Every section leads with the one idea that matters, then backs it up with worked examples and real numbers. If you can work through the practice problems here, you're ready for class, a quiz, or an AP exam.

Ideal for students in AP Physics 1, college Physics 101, or any intro physics course that starts with kinematics. Also useful for tutors prepping a session or parents helping kids get unstuck.

Pick it up, read it in one sitting, and walk into your next exam with a clear head.

What you'll learn
  • Distinguish position, displacement, distance, velocity, speed, and acceleration, and use correct signs in 1D.
  • Read and interpret position-vs-time and velocity-vs-time graphs, including slopes and areas.
  • Apply the four constant-acceleration kinematic equations to solve standard problems.
  • Handle free-fall problems, including objects thrown upward, using g as a constant downward acceleration.
  • Set up problems by choosing a coordinate system, identifying knowns/unknowns, and checking answers for physical sense.
What's inside
  1. 1. Position, Displacement, and the Choice of Axis
    Introduces the 1D coordinate system and the distinction between distance traveled and displacement.
  2. 2. Velocity and Speed: Average vs Instantaneous
    Defines average and instantaneous velocity, contrasts velocity with speed, and connects velocity to the slope of a position-time graph.
  3. 3. Acceleration and Reading Motion Graphs
    Introduces acceleration, explains why negative acceleration isn't always 'slowing down,' and shows how to extract motion information from x-t and v-t graphs.
  4. 4. The Four Constant-Acceleration Equations
    Derives and applies the standard kinematic equations for constant acceleration, with a strategy for choosing which equation to use.
  5. 5. Free Fall and Vertical Motion
    Applies 1D kinematics to objects under gravity, including thrown-upward problems where velocity changes sign.
  6. 6. Problem-Solving Strategy and Common Pitfalls
    A compact playbook for setting up any 1D kinematics problem, plus the mistakes that cost students the most points.
Published by Solid State Press
1D Kinematics: Motion in a Straight Line cover
TLDR STUDY GUIDES

1D Kinematics: Motion in a Straight Line

A High School & College Primer on Position, Velocity, and Acceleration
Solid State Press

1D Kinematics: Motion in a Straight Line

A High School & College Primer on Position, Velocity, and Acceleration

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Who This Book Is For

If you're staring down an AP Physics 1 unit exam, working through motion in a straight line for the first time in an intro physics class, or just trying to make sense of why your textbook needs three pages to explain something that should take three sentences, this guide is for you. It works equally well as a kinematics study guide for high school physics students and as a quick refresher for early college learners.

The book covers every core idea in one-dimensional motion: position, displacement, velocity, speed, and acceleration — with all four constant-acceleration equations and the practice problems you need to actually use them. It also tackles free fall and vertical motion, the topic that trips up more students than any other. Think of it as a focused intro physics kinematics primer built for beginners who want clarity, not volume. About 15 pages, nothing padded.

Read it straight through, work every example alongside the solution, then hit the problem set at the end. That's the whole method.

Contents

  1. 1 Position, Displacement, and the Choice of Axis
  2. 2 Velocity and Speed: Average vs Instantaneous
  3. 3 Acceleration and Reading Motion Graphs
  4. 4 The Four Constant-Acceleration Equations
  5. 5 Free Fall and Vertical Motion
  6. 6 Problem-Solving Strategy and Common Pitfalls
Chapter 1

Position, Displacement, and the Choice of Axis

Before you can describe how something moves, you need a way to say where it is. That requires a coordinate system.

In one-dimensional motion, the coordinate system is just a number line. You pick a point to call zero — the origin — and you pick a positive direction. Every location along the line then gets a single number. That number is the object's position, usually written $x$. Position tells you where the object is relative to the origin, and its sign tells you which side of the origin the object is on.

The choice of origin and positive direction is yours to make. There is no universally "correct" setup. If a car is driving down a highway, you might place the origin at the on-ramp and call east positive. Someone else might place the origin five miles east and call west positive. Both descriptions are valid — the physics works out the same either way. What matters is that you pick a convention and stick with it through the entire problem.

Sign convention is worth pausing on. If rightward (or upward, or eastward — whatever you chose as positive) is the positive direction, then a position of $x = -3 \text{ m}$ simply means the object is 3 meters in the negative direction from the origin. The negative sign carries physical meaning: it encodes direction, not some notion of "bad" or "wrong."

Now, position tells you where an object is. Displacement tells you how its position changed. Formally:

$\Delta x = x_f - x_i$

where $x_f$ is the final position and $x_i$ is the initial position. The Greek letter delta ($\Delta$) always means "final minus initial" — a change in the quantity. Displacement is positive if the object moved in the positive direction, negative if it moved in the negative direction, and zero if the object ended up where it started (regardless of what happened in between).

Keep reading

You've read the first half of Chapter 1. The complete book covers 6 chapters in roughly fifteen pages — readable in one sitting.

Coming soon to Amazon