How to study physics: a routine for solving problems

To study physics, solve problems with a fixed routine: sketch the situation, list knowns and unknowns, choose the principle that applies, rearrange before substituting, and check units and whether the answer makes sense. Use flashcards to remember what each symbol means and when each equation is valid. Reading worked solutions helps little unless you attempt the problem first.

Physics is almost always tested with new situations. You can recognize every formula in the chapter and still freeze on a problem because you cannot tell which one applies. Useful study combines two things: understanding the concepts and practicing the decision about which tool to use.

Repeating the same steps turns problem solving into a habit and makes it easier to find where you went wrong. Write them on the first page of your notebook and follow them even when a problem looks easy.

Our own problem: a car starts from rest and accelerates uniformly at 2 m/s² for 5 s. What speed does it reach and how far does it travel? Knowns: initial velocity 0, acceleration 2 m/s², time 5 s. Because the acceleration is constant, the uniform acceleration equations apply. Final velocity: v = v₀ + a·t = 0 + 2 × 5 = 10 m/s. Distance: d = v₀·t + ½·a·t² = 0 + ½ × 2 × 25 = 25 m.

Check it another way: with constant acceleration, average velocity is the mean of the initial and final values, (0 + 10) ÷ 2 = 5 m/s, and 5 m/s × 5 s = 25 m. The units fit as well: m/s² times s gives m/s, and m/s times s gives m. When two routes give the same answer, the chance of a calculation slip drops sharply.

A card that only asks you to write a formula is quickly forgotten or misused. It is more useful to ask when the formula works: “Under what condition can you use d = v₀·t + ½·a·t²?” Answer: when acceleration is constant over the whole interval. That condition is what saves you on an exam when the problem describes a changing force.

Other cards of this kind separate concepts people mix up: “How are mass and weight different?” Mass is measured in kilograms; weight is a force, measured in newtons, and near Earth's surface it equals W = m·g, with g ≈ 9.8 m/s². A 2 kg object weighs about 19.6 N. Keep the answer short and include a numerical example.

If you solve twenty free-fall problems in a row, the chapter title tells you which equation to use. On the exam, nobody tells you. Rohrer and colleagues (2020) ran a trial with seventh-grade students comparing interleaved math practice with blocked practice, and students who mixed problem types did better on a later test. The study was about math, but choosing a method is exactly the skill physics asks for.

Once you can handle each topic on its own, build sheets that mix kinematics, dynamics and energy problems in random order. Before calculating, write down which principle you will apply. If you choose wrong, that is the error to record, even if the arithmetic afterward is correct.

Dunlosky and colleagues (2013) rated practice testing and spreading study over time as high utility, and rereading and highlighting as low utility. Their review was not about physics, but it describes the usual trap well: reading a worked solution feels like understanding without showing whether you could do it alone.

In practice, spread a topic's problems across several sessions in the week instead of doing them all in one day. Three or four days later, redo the problems you got wrong without looking at the solution. If you can solve them now, you have checked something rereading could never show you.

Some signs tell you that the way you study is not turning into results. Spotting them early saves weeks of practice that does not help.

In Lumia AI you can create a book for the course with blocks or neurons by topic and write cards about conditions, units and easily confused concepts. If you generate a draft from your notes or a PDF, check every equation and condition, because a card that leaves out “constant acceleration” teaches an incomplete rule.

During review, rate each card Again, Hard, Good or Easy and Lumia schedules the next review. You can also run a quiz on the whole book or on a single neuron to check concepts. Problem solving stays on paper: Lumia does not review your handwritten working.