AP Physics 1 Unit 1 Review: Kinematics
Review AP Physics 1 Unit 1 to build the motion toolkit that runs through every unit in the course. From scalar versus vector distinctions to projectile motion in two dimensions, this unit covers the language and equations you need to describe how objects move.
Use the topic guides, practice questions, and FRQ practice available here to work through all five kinematics topics before your exam.
What is AP Physics 1 unit 1?
Kinematics is the foundation of AP Physics 1. Every later unit, from forces to rotational dynamics to oscillations, requires you to describe how position, velocity, and acceleration relate. Unit 1 builds that vocabulary and gives you the graphical, mathematical, and conceptual tools to use it.
Unit 1 covers how to describe motion in one and two dimensions using vectors, kinematic equations, motion graphs, reference frames, and component analysis for projectile motion.
Kinematic equations for constant acceleration
Two-dimensional motion
Any vector can be resolved into perpendicular x and y components using sine and cosine. In projectile motion, the horizontal component has zero acceleration while the vertical component has constant downward acceleration g, so each direction is solved independently.
Kinematics gives you a complete toolkit for describing where an object is, how fast it is moving, and how that motion is changing, all before introducing forces. Understanding the relationships among position, velocity, and acceleration in both one and two dimensions is the prerequisite skill for every quantitative argument in AP Physics 1.
AP Physics 1 unit 1 topics
Scalars and Vectors in One Dimension
Distinguish scalar quantities (distance, speed) from vector quantities (displacement, velocity, acceleration). Use positive and negative signs to encode direction in one-dimensional problems and add vectors algebraically.
Displacement, Velocity, and Acceleration
Define displacement as delta-x = x - x0, average velocity as delta-x / delta-t, and average acceleration as delta-v / delta-t. Recognize that an object accelerates whenever its speed or direction changes, and apply the object model to simplify analysis.
Representing Motion
Use motion diagrams, position-time graphs, velocity-time graphs, and the three constant-acceleration kinematic equations to describe motion. Read slopes and areas off graphs and apply g = 10 m/s^2 for free-fall problems.
Reference Frames and Relative Motion
Identify an observer's inertial reference frame and convert velocities between frames using one-dimensional vector addition. Recognize that velocity is frame-dependent but acceleration is the same in all inertial frames.
Vectors and Motion in Two Dimensions
Resolve vectors into x and y components using sine and cosine, then apply independent one-dimensional kinematics to each direction. Analyze projectile motion by treating horizontal velocity as constant and vertical acceleration as -g.
Hardest AP Physics 1 unit 1 topics
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Across 19k multiple-choice practice attempts for this unit.
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Across 56 scored free-response attempts for this unit.
Hardest topics in unit 1
MCQ miss rateReview Vectors and Motion in Two Dimensions with attention to how the concept appears in AP-style source and evidence questions.
Review Displacement, Velocity, and Acceleration with attention to how the concept appears in AP-style source and evidence questions.
Unit 1 review notes
Scalars and Vectors in One Dimension
Every quantity in kinematics is either a scalar or a vector. Scalars need only a number and a unit. Vectors need a number, a unit, and a direction. In one-dimensional problems, direction is encoded entirely by the sign of the component, so you do not need arrow notation for components along a single axis. When you add vectors in one dimension, opposite directions produce opposite signs, and the result is the algebraic sum.
- Scalar: Magnitude only, no direction. Examples: distance (5 m) and speed (3 m/s).
- Vector: Magnitude and direction. Examples: displacement, velocity, and acceleration. Written with an arrow above the symbol.
- Sign convention in 1D: Choose a positive direction at the start of a problem. Motion opposite to that direction gets a negative sign.
- Vector addition in 1D: Add the signed values algebraically. A displacement of +8 m followed by -3 m gives a net displacement of +5 m.
A car travels 10 m east then 4 m west. What is the distance traveled and what is the displacement? (Distance = 14 m; displacement = +6 m east.)
| Quantity | Type | Example value |
|---|---|---|
| Distance | Scalar | 14 m |
| Speed | Scalar | 3 m/s |
| Displacement | Vector | +6 m |
| Velocity | Vector | -2 m/s |
| Acceleration | Vector | +5 m/s^2 |
Displacement, Velocity, and Acceleration
Displacement is the change in position: delta-x = x - x0. Average velocity is displacement divided by elapsed time. Average acceleration is the change in velocity divided by elapsed time. An object is accelerating whenever its speed changes, its direction changes, or both. As the time interval shrinks toward zero, average values approach instantaneous values. The object model treats any object as a point particle, ignoring size and shape.
- Displacement: delta-x = x - x0. A vector pointing from the initial to the final position.
- Average velocity: v_avg = delta-x / delta-t. Displacement divided by time interval, not total distance divided by time.
- Average acceleration: a_avg = delta-v / delta-t. Change in velocity divided by time interval.
- Instantaneous values: Found by taking the limit as delta-t approaches zero, equivalent to the slope of the tangent on a position-time or velocity-time graph.
- Object model: Treats an object as a single point with mass, ignoring size, shape, and internal structure.
An object moves from x = 2 m to x = -6 m in 4 s. What is its average velocity? (delta-x = -8 m; v_avg = -2 m/s.)
| Quantity | Formula | Units |
|---|---|---|
| Displacement | delta-x = x - x0 | m |
| Average velocity | v_avg = delta-x / delta-t | m/s |
| Average acceleration | a_avg = delta-v / delta-t | m/s^2 |
Representing Motion
Motion can be represented as motion diagrams, position-time graphs, velocity-time graphs, acceleration-time graphs, kinematic equations, or written descriptions. For constant acceleration, three equations link x, v, a, and t. On a position-time graph, slope equals instantaneous velocity. On a velocity-time graph, slope equals acceleration and the area under the curve equals displacement. Free fall near Earth uses a constant downward acceleration of approximately 10 m/s^2.
- vx = vx0 + ax*t: Velocity as a function of time. Use when you know initial velocity, acceleration, and time.
- x = x0 + vx0*t + 0.5*ax*t^2: Position as a function of time. Use when you need displacement and know time.
- vx^2 = vx0^2 + 2*ax*(x - x0): Velocity as a function of position. Use when time is not given or needed.
- Slope on x-t graph: Equals instantaneous velocity. A steeper slope means faster motion; a negative slope means motion in the negative direction.
- Area under v-t graph: Equals displacement over that time interval. Negative area (below the axis) means negative displacement.
A ball is dropped from rest and falls for 3 s. Using g = 10 m/s^2, how far does it fall? (x = 0.5 * 10 * 9 = 45 m.)
| Graph type | Slope equals | Area equals |
|---|---|---|
| Position vs. time | Velocity | N/A |
| Velocity vs. time | Acceleration | Displacement |
| Acceleration vs. time | N/A | Change in velocity |
Reference Frames and Relative Motion
A reference frame is the coordinate system an observer uses to measure motion. Different observers can measure different positions and velocities for the same object depending on their own motion. To convert between frames, add or subtract the observer's velocity as a vector. Crucially, acceleration is the same in all inertial (non-accelerating) reference frames, even when velocities differ.
- Inertial reference frame: A reference frame moving at constant velocity. Newton's laws hold in all inertial frames.
- Relative velocity: v_object relative to ground = v_object relative to observer + v_observer relative to ground. Use signed addition in 1D.
- Frame-dependent velocity: The velocity of an object depends on which frame you measure from. A passenger walking on a train has different velocities relative to the train and to the ground.
- Frame-independent acceleration: All inertial observers measure the same acceleration for an object, even if they disagree on its velocity.
A boat moves at +5 m/s relative to the water. The river flows at +2 m/s relative to the ground. What is the boat's velocity relative to the ground? (+7 m/s.)
| Quantity | Frame-dependent? |
|---|---|
| Position | Yes |
| Velocity | Yes |
| Acceleration | No (same in all inertial frames) |
Vectors and Motion in Two Dimensions
Any vector can be broken into perpendicular x and y components using trigonometry: the x-component uses cosine of the angle and the y-component uses sine of the angle (relative to the horizontal). To find the magnitude of a resultant, use the Pythagorean theorem. In two-dimensional motion, each component is solved with its own one-dimensional kinematics. Projectile motion is the key application: horizontal velocity is constant (ax = 0) and vertical acceleration equals g downward (ay = -10 m/s^2). The two directions share only the time variable.
- Vector resolution: vx = vcos(theta), vy = vsin(theta). Splits a vector into independent perpendicular components.
- Resultant magnitude: v = sqrt(vx^2 + vy^2). Combines components back into a single magnitude.
- Projectile horizontal direction: ax = 0, so vx is constant throughout the flight. Use x = vx0 * t.
- Projectile vertical direction: ay = -g = -10 m/s^2. Use the constant-acceleration kinematic equations with this value.
- Shared time: The time of flight is the same for both components. Solve one direction for time, then use that time in the other direction.
A ball is launched horizontally at 20 m/s from a cliff 45 m high. How long is it in the air, and how far does it travel horizontally? (t = sqrt(245/10) = 3 s; x = 203 = 60 m.)
| Direction | Acceleration | Velocity behavior |
|---|---|---|
| Horizontal (x) | 0 | Constant throughout flight |
| Vertical (y) | -g = -10 m/s^2 | Changes linearly with time |
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Key terms
| Term | Definition |
|---|---|
| scalar | A physical quantity described by magnitude only, without direction. Distance and speed are scalars. |
| object model | A simplification in which an object's size, shape, and internal configuration are ignored and the object is treated as a single point with properties such as mass. |
| position versus time graph | A graph with position on the vertical axis and time on the horizontal axis. The slope at any point equals the instantaneous velocity; a curved line indicates changing velocity. |
| Time in air | The duration an object spends in free fall after being launched, determined solely by the vertical height and gravitational acceleration. |
| Range equation | A kinematic formula relating the horizontal distance traveled by a projectile to its launch speed, launch angle, and gravitational acceleration. |
Common unit 1 mistakes
Confusing distance with displacement
Distance is the total path length (scalar). Displacement is the straight-line change in position (vector). An object that travels 10 m forward and 4 m back has a distance of 14 m but a displacement of only 6 m. Using distance in a velocity formula gives the wrong answer.
Using kinematic equations when acceleration is not constant
The three kinematic equations only apply when acceleration is constant throughout the interval. If a problem describes changing acceleration or multiple phases of motion, you must split the problem into separate constant-acceleration segments.
Mixing up slope and area on motion graphs
On a velocity-time graph, the slope gives acceleration and the area gives displacement, not the other way around. On a position-time graph, the slope gives velocity. Swapping these relationships produces incorrect values.
Forgetting that horizontal velocity is constant in projectile motion
Many students apply g to the horizontal direction or assume the horizontal velocity changes. In projectile motion, ax = 0, so vx stays equal to its initial value for the entire flight.
Subtracting velocities incorrectly in relative motion problems
When converting between reference frames, the sign of the observer's velocity matters. Clearly define a positive direction, write the vector addition equation explicitly, and substitute signed values rather than magnitudes.
How this unit shows up on the AP exam
Graph interpretation and translation
AP Physics 1 frequently asks you to read a position-time or velocity-time graph and describe the motion in words, identify the sign of acceleration, or sketch a corresponding graph in a different representation. Practice moving fluently between graphs, equations, and verbal descriptions for the same motion scenario.
Quantitative justification with kinematic equations
Free-response questions often require you to select the correct kinematic equation, substitute values with correct signs, and show your reasoning. Partial credit depends on setting up the equation correctly even if arithmetic errors occur, so label known and unknown variables explicitly before solving.
Projectile motion analysis in multi-part problems
Two-dimensional kinematics problems typically ask for time of flight, maximum height, or horizontal range in separate parts. Each part may require a different kinematic equation applied to a different direction. Identifying the shared time variable and keeping x and y work clearly separated is the key organizational skill for these problems.
Final unit 1 review checklist
- Classify every quantity as scalar or vector
For any quantity in a problem, confirm whether it needs a direction. Distance and speed are scalars; displacement, velocity, and acceleration are vectors. Assign a positive direction and use signs consistently throughout.
- Apply the three kinematic equations correctly
Identify which of the four variables (x, v, a, t) are known and which is unknown, then select the equation that connects them. Confirm that acceleration is actually constant before using these equations.
- Read motion graphs accurately
On a position-time graph, find velocity from the slope. On a velocity-time graph, find acceleration from the slope and displacement from the area under the curve. Recognize what a curved versus straight line means in each graph type.
- Convert velocities between reference frames
Write out the vector addition equation for relative velocity, assign signs based on your chosen positive direction, and solve algebraically. Confirm that acceleration does not change between inertial frames.
- Resolve vectors into components before solving 2D problems
Use vx = vcos(theta) and vy = vsin(theta) to split any launch velocity. Set up separate kinematic equations for x and y, and identify the shared time variable to link the two directions.
- Handle projectile motion as two independent 1D problems
Horizontal: ax = 0, vx is constant. Vertical: ay = -10 m/s^2, use kinematic equations. Solve for time from one direction and substitute into the other.
- Check signs and units throughout every calculation
A sign error in direction or a unit mismatch (m vs. cm, s vs. ms) is one of the most common sources of wrong answers in kinematics. Label your positive direction at the start and verify units before finalizing.
How to study unit 1
Read the Topic 1.1 guide and practice labeling every quantity in a sample problem as scalar or vector. Write out a few one-dimensional vector addition examples using signed numbers until the sign convention feels automatic.
Work through the Topic 1.2 guide focusing on the formulas delta-x = x - x0, v_avg = delta-x / delta-t, and a_avg = delta-v / delta-t. Practice distinguishing average from instantaneous values and identifying when an object is accelerating.
Use the Topic 1.3 guide to review the three kinematic equations and motion graph interpretation. Sketch position-time and velocity-time graphs for a few scenarios, identify slopes and areas, and solve at least five kinematic equation problems including free-fall.
Read the Topic 1.4 guide and practice the relative velocity addition formula with at least three scenarios involving objects moving in the same and opposite directions. Confirm for each that acceleration is unchanged between frames.
Use the Topic 1.5 guide to practice resolving vectors into components with sine and cosine. Set up and solve at least three projectile motion problems, one with horizontal launch and two with angled launch, keeping x and y equations separate and linking them through time.
More ways to review
Topic study guides
Open the individual guides for Unit 1 when you want a closer review of one topic.
Practice questions
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FRQ practice
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Cram archive videos
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Official unit cheatsheet
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Score calculator
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Unit 1 printables
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get printablesFrequently Asked Questions
What topics are covered in AP Physics 1 Unit 1?
AP Physics 1 Unit 1 covers 5 topics in kinematics: Scalars and Vectors in One Dimension, Displacement, Velocity, and Acceleration, Representing Motion, Reference Frames and Relative Motion, and Vectors and Motion in Two Dimensions. Together they build the foundation for analyzing how objects move in one and two dimensions. Here's a quick breakdown: - **1.1** Scalars and Vectors in One Dimension - **1.2** Displacement, Velocity, and Acceleration - **1.3** Representing Motion (diagrams, graphs, equations) - **1.4** Reference Frames and Relative Motion - **1.5** Vectors and Motion in Two Dimensions See everything for this unit at AP Physics 1 Unit 1.
How much of the AP Physics 1 exam is Unit 1?
Unit 1 makes up 10-15% of the AP Physics 1 exam, making kinematics one of the more heavily tested units. It covers displacement, velocity, acceleration, reference frames, and motion in two dimensions. Expect multiple-choice questions that test graph interpretation and vector analysis, plus free-response questions that ask you to model or explain motion.
What's on the AP Physics 1 Unit 1 progress check (MCQ and FRQ)?
The AP Physics 1 Unit 1 progress check includes both MCQ and FRQ parts drawn from all five kinematics topics: scalars and vectors, displacement, velocity and acceleration, representing motion through graphs and diagrams, reference frames, and two-dimensional motion. The MCQ section tests conceptual understanding and graph reading, while the FRQ section asks you to analyze or model motion scenarios in writing. Practicing with these topics before the progress check is the best prep move. You can find matched practice at AP Physics 1 Unit 1.
How do I practice AP Physics 1 Unit 1 FRQs?
AP Physics 1 Unit 1 FRQs most often pull from displacement and velocity analysis, representing motion with graphs or equations, and two-dimensional vector problems. These questions typically ask you to describe motion, interpret a position-time or velocity-time graph, or solve a multi-step kinematics problem with written justification. To practice effectively, work through problems that require you to both calculate and explain your reasoning in full sentences. College Board scores FRQs on the quality of your explanation, not just the math. Start with the topic guides and practice sets at AP Physics 1 Unit 1 to get reps on each question type.
Where can I find AP Physics 1 Unit 1 practice questions?
The best place to find AP Physics 1 Unit 1 practice questions, including multiple-choice and practice test sets, is AP Physics 1 Unit 1. You'll find MCQ practice covering scalars and vectors, displacement, velocity, acceleration, reference frames, and two-dimensional motion, which are the exact topics tested on the exam. For the most targeted prep, focus on questions that involve reading motion graphs and working with vector components, since those show up most often in both the MCQ and FRQ sections.
How should I study AP Physics 1 Unit 1?
Start by getting solid on displacement and the difference between scalars and vectors, since those ideas run through every other topic in the unit. From there, work through each of the 5 topics in order: one-dimensional vectors, displacement and velocity, motion representations, reference frames, and two-dimensional motion. Here's a study approach that works: 1. **Sketch motion diagrams and graphs** for each scenario before writing equations. Visual models are a huge part of how this unit is tested. 2. **Practice converting between representations**, like going from a position-time graph to a velocity-time graph. 3. **Work FRQs out loud.** Kinematics FRQs reward clear written reasoning, so practice explaining your steps. 4. **Review reference frames carefully.** Relative motion trips up a lot of students but is very testable. All the topic guides and practice you need are at AP Physics 1 Unit 1.