The three questions kinematics answers
Kinematics is the branch of physics that describes motion — without worrying about what causes it (that’s a job for forces, covered elsewhere). It answers three basic questions about a moving object: Where is it? How fast is it going? Is that speed changing?
Position, velocity, and acceleration
- Position is where an object is, relative to some starting point.
- Velocity is how fast position is changing, and in what direction. A car going 60 mph north has a different velocity than one going 60 mph south, even though both have the same speed.
- Acceleration is how fast velocity is changing. Stepping on the gas, hitting the brakes, and turning a steering wheel are all forms of acceleration — even braking, since acceleration just means velocity is changing, not necessarily speeding up.
Distance vs. displacement
These two sound interchangeable, but they aren’t. Distance is the total length of the path you traveled — it only ever adds up, never goes negative. Displacement is how far you ended up from where you started, measured in a straight line, and it has a direction.
Walk 100 meters east, then 100 meters back west, and you’ve covered a distance of 200 meters — but your displacement is zero, because you ended up exactly where you began. This distinction is why “how far did you go?” and “where did you end up?” aren’t the same question in physics.
The kinematic equations
For motion with constant acceleration (a very common starting case), a handful of equations connect position, velocity, acceleration, and time. The most useful one to start with:
v = v₀ + at
In words: your final velocity (v) equals your starting velocity (v₀), plus however much your acceleration (a) has changed it over time (t).
The “Big Five”
That equation is one of five that show up constantly in an intro physics course (often called the “Big Five” in AP Physics 1 prep books, including Princeton Review’s). Together, they relate five quantities: initial velocity (v₀), final velocity (v), acceleration (a), displacement (Δx), and time (t). Each equation happens to leave one of those five out, which is exactly why there are five of them — pick whichever equation skips the one quantity you don’t have.
- v = v₀ + at — leaves out displacement (Δx)
- Δx = v₀t + ½at² — leaves out final velocity (v)
- v² = v₀² + 2aΔx — leaves out time (t)
- Δx = ½(v₀ + v)t — leaves out acceleration (a)
- Δx = vt − ½at² — leaves out initial velocity (v₀)
All five only apply when acceleration is constant — which covers a lot of intro physics problems, but not all of them.
A common mix-up
Speeding up and “positive acceleration” aren’t always the same thing. If a car is moving backward and slowing down, its acceleration actually points forward — it’s still accelerating, just in the direction that reduces its (negative) velocity. Paying attention to direction, not just size, is most of what makes kinematics tricky at first.
Why this matters
Kinematics is the language the rest of mechanics is written in. Before you can figure out why a ball follows the path it does (forces, covered in other Learn topics), you first need a precise way to describe the path itself — that’s exactly what kinematics gives you.
Check your understanding
3 practice questions in the style of AP Physics. Pick an answer to see if you got it, plus a short explanation. Where numbers are needed, use g = 9.81 m/s². These questions were written for this site and are not College Board questions.
1. A runner jogs 100 m east, then turns around and jogs 40 m west. What are the total distance traveled and the displacement?
2. A ball is thrown straight up. At the very top of its flight, which statement is true? (Ignore air resistance.)
3. A car starts from rest and speeds up at a constant 3 m/s² for 4 s. How far does it travel in that time?
Want the real thing? The College Board posts freepast AP Physics 1 exam questions ↗.