Glossary
Average Acceleration Vector
The total change in an object's velocity vector divided by the time interval over which the change occurred.
Example:
If a rocket changes its velocity from straight up to angled, its average acceleration vector points in the direction of that velocity change.
Change in Velocity Vector
The vector difference between an object's final velocity and its initial velocity, indicating both the magnitude and direction of the velocity alteration.
Example:
When a car turns a corner at constant speed, its change in velocity vector is not zero because its direction of motion has changed.
Components (of a vector)
The scalar projections of a vector onto the axes of a coordinate system, allowing for easier mathematical manipulation.
Example:
A force applied at an angle can be broken down into its horizontal and vertical components, which are then used in Newton's second law.
Direction (of a vector)
The orientation of a vector in space, often expressed as an angle relative to a reference axis.
Example:
A projectile launched at a 45° angle above the horizontal has a specific direction for its initial velocity vector.
Displacement
The change in an object's position from its starting point to its ending point, including direction.
Example:
If a bird flies 5 km east from its nest, its displacement is 5 km east, regardless of any detours it took.
Distance
The total path length traveled by an object, regardless of direction.
Example:
A robot vacuum cleaner might travel a total distance of 100 meters cleaning a room, even if it ends up back where it started.
Kinematic Equations (with vectors)
Equations that describe the motion of objects, extended to include vector quantities like displacement, velocity, and acceleration.
Example:
Using kinematic equations with vectors, you can predict the landing spot of a ball thrown at an angle, accounting for both its horizontal and vertical motion.
Magnitude (of a vector)
The scalar size or length of a vector, representing its quantity without direction.
Example:
If a force vector is N, its magnitude is 5 N, calculated using the Pythagorean theorem.
Scalars
Physical quantities that possess only magnitude (size) and no direction.
Example:
The mass of a bowling ball is 6 kg, which is a scalar quantity because it only describes how much 'stuff' it contains, not a direction.
Speed
The rate at which an object covers distance, a scalar quantity.
Example:
A cheetah can reach a speed of 120 km/h, indicating how fast it's moving without specifying its direction.
Unit Vectors
Dimensionless vectors with a magnitude of one, used to specify directions in a coordinate system (e.g., $\hat{i}$ for x, $\hat{j}$ for y, $\hat{k}$ for z).
Example:
To describe a force acting purely along the positive y-axis, you might write it as N, where is the unit vector in the y-direction.
Vector Addition
The process of combining two or more vectors to find a single resultant vector, considering both their magnitudes and directions.
Example:
When a boat travels across a river, its vector addition of its velocity relative to the water and the river's current velocity determines its actual path relative to the ground.
Vector Notation
A symbolic representation of a vector, typically using an arrow above the variable (e.g., $\vec{A}$) or boldface type.
Example:
In physics problems, the acceleration of gravity is often written as to emphasize its vector nature, pointing downwards.
Vector Subtraction
The process of finding the difference between two vectors, equivalent to adding the negative of the second vector.
Example:
To find the change in velocity of a car that brakes, you perform vector subtraction of its final velocity from its initial velocity.
Vectors
Physical quantities that possess both magnitude (size) and direction.
Example:
When a car moves 50 km north, its movement is described by a vector, indicating both the distance traveled and the specific direction.
Velocity
The rate at which an object changes its displacement, a vector quantity that includes both speed and direction.
Example:
A sailboat moving at 15 knots northwest has a specific velocity, combining its speed with its heading.