1.1 Scalars and Vectors in One Dimension
Before we can analyze how objects move, we must understand the quantities we use to describe that motion. In physics, measurable quantities are divided into two main categories: scalars and vectors.
Scalar Quantity: A physical quantity that has only a magnitude (a number and a unit). It does not include direction.
Vector Quantity: A physical quantity that has both a magnitude and a direction in space.
Comparing Key Quantities
| Scalars (Magnitude Only) | Vectors (Magnitude + Direction) |
|---|---|
| Distance (d) | Displacement (Δx) |
| How much ground an object has covered during its motion. (e.g., "50 meters") | The overall change in position of the object. (e.g., "50 meters North") |
| Speed (v) | Velocity (vā) |
| How fast an object is moving. Distance divided by time. | The rate at which position changes. Displacement divided by time. |
| Time (t), Mass (m), Temperature (T) | Acceleration (aā), Force (Fā) |
Thought Experiment: The Track Runner
If an athlete runs one complete lap around a 400-meter track and finishes exactly where they started:
- Their distance traveled is 400m.
- Their displacement is 0m (because their start and end positions are the same).
1.2 Displacement, Velocity, and Acceleration
Kinematics is the study of motion without considering its causes (forces). We rely on three fundamental concepts linked by mathematical definitions.
Velocity
The rate of change of position.
Acceleration
The rate of change of velocity.
The Kinematic Equations (Constant Acceleration)
When acceleration is constant, we use the "Big Three" kinematic equations. These are provided on your AP Physics 1 equation sheet.
(Use when missing position, x)
(Use when missing final velocity, v)
(Use when missing time, t)
ā ļø Speeding Up vs. Slowing Down:
An object speeds up when its velocity and acceleration vectors point in the same direction (both positive OR both negative).
An object slows down when velocity and acceleration point in opposite directions.
1.3 Representing Motion
Graphical representations of motion are heavily tested on the AP Physics 1 exam. You must be able to translate between Position-Time, Velocity-Time, and Acceleration-Time graphs.
The Golden Rules of Kinematic Graphs
1. Slopes (Derivatives):
- The slope of a Position vs. Time graph is the Velocity.
- The slope of a Velocity vs. Time graph is the Acceleration.
2. Areas (Integrals):
- The area under an Acceleration vs. Time graph is the Change in Velocity (Δv).
- The area under a Velocity vs. Time graph is the Displacement (Δx).
šÆ Translating Graphs: If a position-time graph curves like a parabola (opening upwards), the slope is increasing. This means velocity is increasing, which means the acceleration is positive and constant!
1.4 Reference Frames and Relative Motion
Motion is relative. How fast an object appears to be moving depends on the observer's frame of reference.
Inertial Reference Frame: A frame of reference that is not accelerating. Newton's laws hold true in all inertial frames.
Relative Velocity Equation
If you need to find the velocity of object A relative to object C, and you know the velocities relative to an intermediate frame B, you can add the velocity vectors:
Example: You are walking forward at 2 m/s (relative to a train) inside a train that is moving forward at 15 m/s (relative to the ground).
ā¢ vYou, Train = +2 m/s
ā¢ vTrain, Ground = +15 m/s
Your velocity relative to the ground is:
vYou, Ground = vYou, Train + vTrain, Ground = 2 + 15 = +17 m/s
1.5 Vectors and Motion in Two Dimensions
When motion occurs in two dimensions (like a projectile arcing through the air), we must break the motion down into separate, independent 1D components using trigonometry.
Resolving Vectors into Components
Any vector can be split into a horizontal (x) and vertical (y) component.
X-Component
Y-Component
Projectile Motion
The core rule of projectile motion is that perpendicular components of motion are completely independent of each other. They only share one variable: Time (t).
| Horizontal (x) Motion | Vertical (y) Motion |
|---|---|
| Constant Velocity | Constant Acceleration |
| Acceleration in x is zero (ax = 0). Air resistance is ignored unless stated otherwise. | Acceleration in y is due to gravity (ay = -g, or approx -9.8 m/s2). |
The equation simplifies to:Δx = vxt |
Use all three kinematic equations. |
Unit 1 Key Takeaways
Acceleration is the rate of change of velocity, not speed.
Slowing down means velocity and acceleration have opposite signs.
Area under a v-t graph = Displacement.
Slope of a v-t graph = Acceleration.
In 2D projectile motion, horizontal velocity (vx) remains constant!
Time (t) is the bridge between horizontal and vertical motion equations.
End of Unit 1 Study Guide.