A one-page summary of Kinematics — the kinematic equations, motion graphs, scalars vs. vectors, reference frames, and projectile motion. Everything you need at a glance.
Exam weight: About 10–15% of the AP Physics 1 exam
The big question: How do we describe HOW an object moves through space and time — without worrying yet about WHY it moves?
Value of g for the exam: 10 m/s² downward (9.8 or 9.81 also accepted)
📐 The kinematic equations (constant acceleration)
v = v₀ + at
Final velocity from initial velocity, acceleration, and time. Use when you don't have displacement.
x = x₀ + v₀t + ½at²
Position from initial position, initial velocity, acceleration, and time. Use when you don't have final velocity.
v² = v₀² + 2a(x − x₀)
Final velocity squared from initial velocity, acceleration, and displacement. Use when you don't have (or need) time.
v_avg = Δx / Δt
Average velocity = displacement divided by time interval. (Vector — same direction as Δx.)
a_avg = Δv / Δt
Average acceleration = change in velocity divided by time interval. (Vector — same direction as Δv.)
The 5 topics at a glance
1.1 Scalars & Vectors (1D)
Scalars have magnitude only (distance, speed). Vectors have both magnitude and direction (displacement, velocity, acceleration). In 1D, use + and − signs for direction.
1.2 Displacement, Velocity, Acceleration
Displacement = change in position. Velocity = rate of change of position. Acceleration = rate of change of velocity. Average vs. instantaneous depends on the time interval.
1.3 Representing Motion
Motion diagrams, kinematic equations, and motion graphs. Slope of x-t = v; slope of v-t = a; area under v-t = Δx; area under a-t = Δv. Near Earth: g ≈ 10 m/s² downward.
1.4 Reference Frames & Relative Motion
Different observers measure different velocities, but they all agree on acceleration. Add or subtract velocities to convert between frames. AP Physics 1 tests this in 1D only.
1.5 Vectors & 2D Motion
Break vectors into x- and y-components using cos and sin. Solve 2D motion as two independent 1D problems. Projectile motion: zero horizontal acceleration, vertical acceleration = g.
Connecting It All
Kinematics is the language for describing motion. Every other unit (forces, energy, momentum) uses these tools. Master the graphs and equations early — they'll save you on the exam.
📊 Motion graphs: what to remember
Position-time (x-t) graph — the SLOPE at any point equals velocity. Curved lines mean velocity is changing (i.e., acceleration).
Velocity-time (v-t) graph — the SLOPE equals acceleration. The AREA UNDER THE CURVE equals displacement.
Acceleration-time (a-t) graph — the AREA UNDER THE CURVE equals the change in velocity.
Slope and area conversions always work together: take a derivative (slope) to go x → v → a; integrate (area) to go a → v → x.
Above the time axis = positive direction; below = negative direction.
🎯 Projectile motion: the rules
Horizontal motion: zero acceleration. Horizontal velocity stays constant the whole flight.
The two motions are independent — solve each direction separately with the kinematic equations.
Time is the link — the only thing horizontal and vertical motions share is how long the projectile is in the air.
At the peak: vertical velocity = 0, but horizontal velocity is unchanged (so total velocity is NOT zero).
Trajectory is a parabola (when air resistance is ignored).
The key terms you must know
Scalar — magnitude only (distance, speed, time, mass).
Vector — magnitude AND direction (displacement, velocity, acceleration, force).
Displacement (Δx) — change in position; can be positive or negative; NOT the same as distance.
Velocity — rate of change of position (vector). Speed is just its magnitude.
Acceleration — rate of change of velocity (vector). Occurs when speed OR direction changes.
Free fall — motion under gravity only; a = g downward.
Reference frame — the observer's point of view; different frames measure different velocities but the same acceleration.
Projectile motion — 2D motion under gravity only; horizontal a = 0, vertical a = −g.
⚠️ Common exam traps
Distance vs. displacement — a hiker who walks 3 km north and 3 km south has 6 km distance but 0 m displacement.
"Zero velocity" doesn't mean "zero acceleration" — a ball at the top of its arc has v = 0 but a = g downward.
Negative acceleration ≠ slowing down — it just means acceleration points in the negative direction. An object speeding up in the negative direction has negative acceleration.
Constant speed can still be accelerating — a car turning at 30 mph has constant speed but changing direction = changing velocity = acceleration.
Don't forget time is shared in 2D motion — use vertical motion to find time, then plug into horizontal motion (or vice versa).
Slope of x-t graph is velocity, not position. The value of x at that point is the position; the slope is velocity.