Kinematics equations are the set of formulas relating displacement, initial and final velocity, acceleration, and time for an object moving with constant acceleration, letting you solve for any unknown motion quantity in AP Physics 1 problems like free fall and projectile motion.
Kinematics equations are the math toolkit for describing motion when acceleration is constant. There are four of them, and each one connects four of the five motion variables (displacement Δx, initial velocity v₀, final velocity v, acceleration a, and time t):
The trick to using them is bookkeeping. Each equation is missing exactly one variable, so you list what you know, identify what you want, and pick the equation that skips the variable you don't care about. The catch, and it's a big one on the AP exam, is that these equations only work when acceleration is constant. Free fall near Earth's surface (a = g ≈ 10 m/s² downward) and projectile motion both qualify, which is why kinematics equations show up everywhere in Unit 1. They describe how things move without ever asking why. Forces are a different unit's problem.
Kinematics equations are the backbone of Unit 1 (Kinematics) in AP Physics 1, where you're expected to describe motion using representations like graphs, equations, and diagrams, and to calculate unknown quantities for objects with constant acceleration. But their real value is that they never go away. Unit 2 dynamics problems routinely hand you forces, expect you to find acceleration with Newton's second law, then make you plug that acceleration into a kinematics equation to find a distance or time. Projectile motion is just kinematics run twice, once for each direction. And in Unit 5, the exact same four equations come back wearing rotational costumes (θ, ω, α instead of x, v, a). If you can pick the right kinematics equation quickly, you've unlocked a chunk of the entire course.
Keep studying AP Physics 1 Unit 1
Free Fall (Unit 1)
Free fall is the cleanest possible kinematics problem because the acceleration is always the same, g ≈ 10 m/s² pointing down. Every dropped-ball or thrown-upward problem is just a kinematics equation with a already filled in for you.
Projectile Motion (Unit 1)
A projectile problem is two kinematics problems stapled together. Horizontally, acceleration is zero so velocity is constant; vertically, it's free fall. You solve each direction separately with the same equations, and time is the variable that links them.
Acceleration (Unit 1)
Acceleration is the variable the whole equation set is built around. The 'constant acceleration' condition isn't fine print, it's the entire reason these four specific equations exist. If a changes over time, you need graphs or calculus-free reasoning instead.
Newton's Second Law and Dynamics (Unit 2)
The classic two-step AP problem goes: use F = ma to find acceleration, then use kinematics to find how far or how fast. Dynamics tells you what the acceleration is; kinematics tells you what that acceleration does to the motion.
Rotational Kinematics (Unit 5)
Swap x for θ, v for ω, and a for α, and you get the rotational kinematics equations. Same structure, same constant-acceleration rule, same strategy for picking which equation to use. Learn them once, use them twice.
On multiple choice, kinematics equations show up directly (calculate the stopping distance, the time in the air, the final speed) and conceptually (which equation applies, what a velocity-time graph implies about displacement). On free-response questions, they're usually the closing move of a multi-step problem. A typical FRQ gives you a force situation, asks you to derive acceleration symbolically, then has you find a displacement or time using kinematics. Two things earn points consistently. First, check that acceleration is actually constant before using these equations, because applying them to a varying force situation is a classic way to lose credit. Second, keep your signs straight by defining a positive direction up front, especially in free fall where v and a can point opposite ways. Symbolic answers matter too, since the revised exam loves asking you to derive expressions in terms of given variables rather than crunch numbers.
Kinematics describes motion; dynamics explains it. Kinematics equations relate displacement, velocity, acceleration, and time without ever mentioning a force. Newton's second law (F = ma) tells you where the acceleration comes from. On the exam they work as a relay team. Dynamics hands you the acceleration, and kinematics carries it the rest of the way to a distance, speed, or time. If a problem gives forces or masses, start with Newton; if it gives only motion quantities, you're in pure kinematics territory.
The kinematics equations only apply when acceleration is constant, so always check that condition before using them.
Each of the four equations is missing exactly one motion variable, so pick the equation that omits the quantity you neither know nor need.
Free fall and projectile motion are both constant-acceleration situations with a = g ≈ 10 m/s² downward, which makes them prime kinematics-equation territory.
In projectile motion, apply kinematics separately to the horizontal direction (a = 0) and the vertical direction (a = g), connected by the shared time of flight.
Sign conventions matter: define a positive direction first, because an object thrown upward has positive velocity but negative acceleration in that frame.
The same equation structure returns in Unit 5 as rotational kinematics, with θ, ω, and α replacing x, v, and a.
They are the four constant-acceleration equations: v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx, and Δx = ½(v₀ + v)t. Each relates four of the five motion variables (displacement, initial velocity, final velocity, acceleration, time) and leaves one out.
No. The four kinematics equations are derived assuming constant acceleration, so using them on a varying force (like a spring or changing friction) gives wrong answers. For non-constant acceleration in AP Physics 1, use velocity-time graphs, energy methods, or break the motion into constant-acceleration chunks.
List the variables you know and the one you want, then pick the equation that doesn't contain the variable you're missing. For example, if a problem never mentions time, reach for v² = v₀² + 2aΔx, the only equation without t.
Kinematics describes motion using displacement, velocity, acceleration, and time, without asking why the motion happens. Dynamics (Unit 2) uses forces and Newton's second law to explain where acceleration comes from. AP problems often chain them: find a from forces, then plug it into kinematics.
Yes, the equation sheet includes the constant-acceleration kinematics equations, so you don't have to memorize them word for word. But the exam tests whether you can choose the right one, handle signs and directions, and recognize when the constant-acceleration condition fails, none of which the sheet does for you.