Physics without mysteries

On a desk or in a notebook another motion problem appears: constant speed one day, braking the next, a ball from a roof after that. It is easy to lose track of which formula to open first. This series lays out eight topics in a clear order, with an example and a calculator for each part.

Physics without mysteries is a path through kinematics, simple F = m·a and energy. Each part has a clear model, a few formulas, typical traps and an example you can check in a calculator.

The series does not replace a textbook. It organises the choice: you know where to start, when s = v·t is allowed, and when you must move to constant a or to g = const. The goal is practical: finish the calculation without guessing which page to open.

The order is deliberate. Parts 1-3 build the language of straight-line motion: constant v, then constant a while speeding up, then deceleration while braking. Only then does gravity enter in the throws (parts 4-6), the incline (7) and the balance of Ek, Ep and work (8).

You can read selectively if you are returning to one topic. If you are learning from scratch, keep the order. Formulas from parts 1-3 return in the throws as motion components and as the intuition for “distance at constant acceleration”.

Part 1 (uniform motion) teaches the trio v, s, t at constant v:

s = v·t

A micro-check from that part: v = 20 m/s for t = 90 s gives s = 1800 m. That is about 72 km/h for a minute and a half. The same order of magnitude returns later in the reaction-time stretch before braking.

Part 2 (accelerated motion) adds v₀, a and s = v₀·t + ½·a·t². Part 3 (braking) flips the sign of acceleration and shows stopping distance plus bridges to momentum and work.

A speeding-up example: a = 3.5 m/s² and t = 8 s with v₀ = 0 give v_k = 28 m/s (about 100 km/h) and s = 112 m. Someone who multiplies final v by t gets twice too much. That trap returns in every constant-a part.

Parts 4-6 are three throw models at constant g with no air drag: vertical, horizontal from a height, and angled. The vertical, horizontal and angled comparison keeps them side by side in one table so you do not mix H_max with range Z.

A shared throw micro-check: v₀ = 10 m/s and g = 9.81 m/s². Vertically, H_max ≈ 5.1 m. Horizontally from h ≈ 5.1 m, range Z ≈ 10.2 m. At 45° on flat ground Z ≈ 10.2 m, but H_max ≈ 2.55 m. One speed, three different stories.

Part 7 moves constant a onto the incline: a = g·sin α without friction and a μ variant. Part 8 closes the loop with energy: Ek = ½·m·v², Ep = m·g·h and work W = F·s. Same motion, different balance language.

Shared assumptions for almost the whole series: motion in one dimension or in a plane (throws), SI units (m, s, m/s, m/s², N, J), g usually 9.81 m/s², air drag off unless the problem says otherwise. When the model is too tight, the article says which calculator to use instead of the “flat” formula.

Tools stay split on purpose. A “distance only” page does not replace full v-s-t. A range calculator does not replace the full path with h₀ > 0. This series teaches when each link makes sense, instead of dumping everything onto one screen.

How to use the guide: first read the short intro on the part page, then the theory, then the example. If the calculator disagrees with your paper, check units (km/h versus m/s) and the sign of acceleration before you change the model.

The series boundary is deliberate. There is no relativity, varying g or heavy drag modeling here. There is an honest “this is enough for most everyday calculations on kinematics and simple F = m·a”.

If you want a topic map instead of a numbered path, go to kinematics from scratch. There the nodes are arranged by idea (average speed, acceleration, energy), not by part number.

Treat parts 1-3 as the alphabet. Without a solid s = v·t it is easy to misread a graph in a horizontal throw. Without s = v₀·t + ½·a·t² it is harder to see that the vertical part of an angled throw is the same accelerated motion with constant g. Braking adds v²/(2a), which soon returns as H_max = v₀²/(2g).

In practice it is tempting to jump straight to “the range formula”. The series delays that jump on purpose. First you learn to name the model and list data in matching units. Only then do you open the calculator. That order cuts random clicks on the wrong tool type.

The series is bilingual by design. PL and EN share the same models and example numbers. When you learn English terms (range, deceleration, incline), switch version and keep the same line of thought.

The series does not compete with textbook problems. It supports them. When you stall on “is this average or instantaneous?”, go back to part 1 and the kinematics map. When you stall on “tower or flat range?”, go back to the throw comparison.

It is worth returning to this guide after each larger topic block. Mark which parts went smoothly and which needed the FAQ. The series is short enough to walk twice: once from part 1, once against what you are working on now.

If you pair a calculator with a notebook, write a short model next to the answer: “v=const”, “a=const”, “g=const, h0=0”. That habit matters more than memorising every rearrangement at once. The table below leads to the eight parts in the recommended order.

For practice one ritual is enough: name the model, list data in matching units, open the right part and check order of magnitude. At 20 m/s, distance in 90 s should be about 1800 m. At 10 m/s vertically, height should be a few meters. When a result is two orders off, look for units first, not a new formula.

The table below is a path index, not a substitute for the articles. Each part has its own assumptions, FAQ and example. This guide sets the order when you lose the thread between v, a and g.