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AP Physics 1: Algebra-Based · Unit 1 of 8
Kinematics
10–15% of the exam4 lessons · 53 min24 terms
What this unit covers
The topics below follow the published Physics 1 course framework for Unit 1. This unit is worth 10–15% of the exam, so budget your time against that rather than against how long the unit takes to teach.
Position & velocityAccelerationProjectile motionGraphs of motion
Lessons in this unit
- Position, Displacement & Velocity12 min · 3 objectivesDistinguish position, distance, and displacement using a sign convention · Compute displacement as a change in position, Δx = x_f − x_i · Calculate average velocity and contrast it with average speed
- Acceleration & the Kinematic Equations14 min · 3 objectivesDefine acceleration as the rate of change of velocity · Select the correct kinematic equation from the known and unknown quantities · Solve constant-acceleration problems, including braking to a stop
- Reading Motion Graphs13 min · 3 objectivesInterpret the slope of a position–time graph as velocity · Interpret the slope of a velocity–time graph as acceleration · Find displacement from the area under a velocity–time graph
- Projectile Motion14 min · 3 objectivesTreat horizontal and vertical motion as independent · Analyze a horizontally launched projectile using time as the shared variable · Explain why horizontal velocity stays constant while vertical velocity changes
Formulas in Unit 1
Displacement
Δx = x_f − x_i
Final minus initial. A negative result simply means motion in the negative direction, not "less than zero distance".
Average velocity
v_avg = Δx / Δt = (x_f − x_i) / (t_f − t_i)
Units: meters per second, m/s. The sign of v_avg is the sign of Δx.
Velocity–time (no Δx)
v = v₀ + at
Use when you have or want time but not displacement.
Position–time (no v)
Δx = v₀t + ½at²
The ½ is not optional — dropping it is the single most common kinematics mistake.
Timeless equation (no t)
v² = v₀² + 2aΔx
The rescue equation when time is neither given nor asked for.
Slope and area
slope of x–t = v · slope of v–t = a · area under v–t = Δx
Two different graphs, three different meanings — keep straight which graph you are reading.
Projectile equations (horizontal launch, taking down as +)
horizontal: Δx = v_x·t · vertical: Δy = ½g·t² · v_y = g·t
No acceleration horizontally (v_x constant); a = g ≈ 10 m/s² vertically.
Every term in Unit 1
All 24 terms we publish for Kinematics, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.
- Scalar vs vector
- Scalars have magnitude only (speed, distance, mass); vectors have magnitude and direction (velocity, displacement, force).
- Displacement vs distance
- Displacement is the straight-line change in position and can be zero on a round trip; distance is total path length and never decreases.
- Average vs instantaneous velocity
- Average velocity is displacement over elapsed time; instantaneous velocity is the slope of the position-time graph at one instant.
- Acceleration
- Rate of change of velocity. An object slowing down has acceleration opposite its velocity — acceleration is not "speeding up".
- Kinematic equations condition
- v = v₀ + at, x = x₀ + v₀t + ½at², v² = v₀² + 2aΔx. All require CONSTANT acceleration; they are wrong otherwise.
- Position-time graph
- Slope is velocity. A curved graph means changing velocity, so acceleration is non-zero.
- Velocity-time graph
- Slope is acceleration and the area under the curve is displacement. Area below the axis counts as negative displacement.
- Free fall
- Acceleration is g ≈ 9.8 m/s² downward throughout, including at the top of the flight where velocity is momentarily zero.
- Projectile motion independence
- Horizontal and vertical motions are independent, sharing only the time. Horizontal velocity is constant; vertical acceleration is g.
- Time of flight for a projectile
- Determined entirely by the vertical motion. A ball thrown horizontally and one dropped from the same height land together.
- Range of a projectile
- Horizontal velocity times time of flight. For level ground, 45° maximizes range for a given launch speed.
- Relative motion
- Velocity depends on the reference frame. v_AC = v_AB + v_BC — velocities add as vectors, not as numbers.
- Vector components
- A vector at angle θ has components v cos θ along x and v sin θ along y. Adding vectors means adding components separately.
- Reading a graph to find another quantity
- Slope gives the derivative and area gives the integral: position → velocity → acceleration by slope, and back by area.
- Linearizing data
- Rewrite the relationship so it has the form y = mx + b, then plot those quantities. Plotting d against t² for free fall gives a straight line of slope ½g.
- Slope with units
- Always state what the slope of a graph physically represents and its units. A velocity-time slope of 2.4 is 2.4 m/s², not just "2.4".
- Best-fit line vs connecting dots
- A best-fit line averages out random error; connecting points treats every measurement as exact and hides the trend.
- Systematic vs random error
- Systematic error shifts every measurement the same way and does not shrink with repetition; random error scatters and does shrink when results are averaged.
- Identifying the independent variable
- The quantity you deliberately change; it belongs on the horizontal axis. The dependent variable is what you measure in response.
- Control variable
- A quantity deliberately held constant so it cannot explain the observed change. Naming one is worth a point on nearly every design question.
- Reducing uncertainty in timing
- Time many cycles and divide, rather than timing one. Human reaction error is a fixed amount, so spreading it over ten cycles cuts its effect tenfold.
- Instantaneous velocity from a position graph
- Draw a tangent at the instant and take its slope. The secant slope between two nearby points approximates it.
- Sign conventions
- Choose a positive direction and use it consistently. A negative acceleration means "toward the negative direction", not necessarily "slowing down".
- Interpreting a curved velocity-time graph
- Curvature means acceleration is changing, so the kinematic equations do not apply and area must be estimated geometrically.
What examiners penalize here
- On the AP exam, always state your positive direction before plugging in numbers. Half of kinematics is bookkeeping — a consistent sign convention earns points that raw algebra cannot.
- When a problem gives you velocities and a distance but never mentions time, reach straight for v² = v₀² + 2aΔx. Recognizing that missing variable saves you from solving a needless quadratic.
- Free-response graph questions love the chain "slope of x–t → v, slope of v–t → a, area under v–t → Δx". Memorize those three links and you can convert between any pair of graphs.
- The classic AP trap: applying gravity to the horizontal axis. Horizontal velocity is constant for every projectile. Gravity changes only the vertical velocity. Keep the two axes in separate columns on your paper.
Practice Physics 1
Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.
Questions about this unit
How much of the AP Physics 1: Algebra-Based exam is Unit 1?
Unit 1, Kinematics, is worth 10–15% of the Physics 1 multiple-choice section according to the published course framework. Across all 8 units that makes it a substantial share — heavier than an even split would give it.
What topics are covered in Physics 1 Unit 1?
Kinematics covers Position & velocity, Acceleration, Projectile motion and Graphs of motion. We publish 24 terms with definitions for this unit, all of them on this page.
How should I study Physics 1 Unit 1?
Read the 4 lessons below first — about 55 minutes — then drill the 24 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.
All 8 units of AP Physics 1: Algebra-Based
Unit names, topics and exam weights follow the published College Board course framework for AP Physics 1: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.