A vector quantity is a physical quantity described by both magnitude and direction, drawn as an arrow whose length is proportional to its size; in AP Physics 1, position, displacement, velocity, and acceleration are vectors, while distance and speed are scalars (CED 1.1.A).
A vector quantity is any physical quantity that needs two pieces of information to fully describe it: how much (magnitude) and which way (direction). "5 m/s" is incomplete for velocity. "5 m/s east" is the full vector. The CED (1.1.A) names position, displacement, velocity, and acceleration as the core examples, and contrasts them with scalars like distance and speed, which only have magnitude.
You model vectors as arrows. The arrow's length is proportional to the magnitude, and the arrow points in the quantity's direction. In notation, a vector gets an arrow over its symbol, like . Here's the practical payoff in one dimension (1.1.B): opposite directions get opposite signs. So a ball thrown upward at +10 m/s while gravity pulls with acceleration of -9.8 m/s² isn't a contradiction. The signs ARE the directions. Adding vectors in 1D is just adding signed numbers, which is why a negative velocity or negative acceleration on the AP exam is telling you about direction, not about "slowing down."
This term lives in Topic 1.1 (Position, Velocity, and Acceleration) and is the direct target of learning objective AP Physics 1 Revised 1.1.A, which asks you to describe a scalar or vector quantity using magnitude and direction as appropriate, and 1.1.B, which asks you to describe a vector sum in one dimension. But it's really the operating system for the whole course. Every kinematics equation, like , is a vector equation. Forces are vectors, so Newton's second law only works if you track directions with signs or components. Even in Unit 8, the buoyant force is defined directionally as a net upward force (8.3.B.1). If you treat vectors as scalars, you'll add magnitudes that should cancel, and that's one of the most common point-losing mistakes on the exam.
Keep studying AP Physics 1 Unit 8
Scalar Quantity (Unit 1)
Scalars are the other half of CED 1.1.A. Distance and speed are the scalar shadows of displacement and velocity. A runner who does one full lap covers a big distance (scalar) but has zero displacement (vector), because the start and end arrows land on the same point. That mismatch is a classic MCQ trap.
Displacement and Velocity (Unit 1)
These are the first vectors you actually compute with. In one dimension, direction becomes a sign, so a velocity of -3 m/s just means motion in the negative direction. An object with negative velocity and negative acceleration is speeding up, not slowing down, because both vectors point the same way.
Centripetal Acceleration (Unit 3)
Uniform circular motion is the ultimate proof that velocity is a vector. The speed (magnitude) stays constant, but the direction constantly changes, so the object is accelerating the entire time. Centripetal acceleration exists purely because direction counts.
Buoyant Force (Unit 8)
The CED defines the buoyant force as a net upward force (8.3.B.1). It's a vector sum in disguise. Fluid particles push on the object from every side, and the upward pushes from below win out over the downward pushes from above. Drop the directions and the whole concept collapses.
No released FRQ asks you to define "vector quantity" verbatim, but vector reasoning is baked into nearly every question. Multiple-choice stems test it through signs: "the velocity is positive and the acceleration is negative, so the object is..." You also see it in graph questions, where a velocity-time graph dipping below the axis means the direction reversed. On FRQs, vector thinking shows up whenever you draw a free-body diagram, choose a positive direction, or justify why two quantities cancel. The skill the exam actually rewards is consistency. Pick a coordinate system, assign opposite signs to opposite directions (1.1.B), and stick with it. One helpful note from the CED: vector notation isn't required for components along an axis, so in 1D problems, signed values like m/s are completely acceptable.
A scalar has magnitude only; a vector has magnitude and direction. Speed is a scalar, velocity is a vector. Distance is a scalar, displacement is a vector. The test: if reversing direction would change the quantity, it's a vector. Walking 3 m east then 3 m west gives a distance of 6 m (scalar, directions don't matter) but a displacement of 0 m (vector, the directions cancel). On the exam, any time a question swaps "speed" for "velocity" or "distance" for "displacement," check whether direction changes the answer. It usually does.
A vector quantity has both magnitude and direction, while a scalar quantity has magnitude only.
Position, displacement, velocity, and acceleration are vectors; distance and speed are their scalar counterparts.
Vectors are drawn as arrows whose length is proportional to the magnitude, and notated with an arrow over the symbol, like .
In one dimension, opposite directions get opposite signs, so adding vectors is just adding signed numbers.
A negative sign on velocity or acceleration tells you direction, not whether the object is slowing down; an object with negative velocity and negative acceleration is speeding up.
An object moving at constant speed in a circle is still accelerating, because the direction of its velocity vector is changing.
A vector quantity is a physical quantity with both magnitude and direction, modeled as an arrow whose length is proportional to its size. The CED's core examples are position, displacement, velocity, and acceleration (1.1.A).
No. Speed is a scalar because it has magnitude only. Velocity is the vector version, since it includes direction. A car going 30 m/s has a speed; a car going 30 m/s north has a velocity.
No, and this is one of the most common AP Physics 1 misconceptions. Negative acceleration just means the acceleration vector points in the negative direction. If velocity is also negative, the object is actually speeding up.
A vector needs both magnitude and direction; a scalar needs only magnitude. Quick test: walk 3 m east then 3 m west. Your distance (scalar) is 6 m, but your displacement (vector) is 0 m because the opposite directions cancel.
Assign opposite signs to opposite directions, then add the signed values (CED 1.1.B). For example, +10 m/s and -4 m/s combine to +6 m/s. The CED notes you don't need formal vector notation for components along a single axis.