Glossary
Acceleration
The rate of change of an object's velocity over time, indicating how quickly its velocity is changing in magnitude or direction. It is a vector quantity.
Example:
When a roller coaster speeds up down a hill, it experiences positive acceleration; when it slows down at the top, it experiences negative acceleration.
Acceleration vs. Time Graph
A graph that plots an object's acceleration on the y-axis against time on the x-axis, where the area under the curve represents the change in velocity.
Example:
A constant positive value on an acceleration vs. time graph indicates uniform acceleration, like a car steadily speeding up.
Average Velocity
The total displacement of an object divided by the total time interval over which the displacement occurred.
Example:
If a runner completes a 400-meter lap in 50 seconds, their average velocity for the lap is 0 m/s because their net displacement is zero.
Derivatives (in Kinematics)
A mathematical tool used to find the instantaneous rate of change of one quantity with respect to another, such as velocity from position or acceleration from velocity.
Example:
Taking the derivative of a car's position function x(t) = 3t² + 2t will give you its velocity function v(t) = 6t + 2.
Displacement (Δx)
The change in an object's position, measured as the straight-line distance and direction from its initial to its final point. It is a vector quantity.
Example:
Walking 5 meters east and then 5 meters west results in a zero displacement, even though you walked 10 meters.
Distance
The total path length covered by an object during its motion, regardless of direction. It is a scalar quantity.
Example:
If a robot travels 3 meters forward and then 2 meters backward, the total distance traveled is 5 meters.
Instantaneous Velocity
The velocity of an object at a specific moment in time, found by taking the derivative of the position function with respect to time.
Example:
The reading on a car's speedometer at any given moment tells you its instantaneous velocity.
Integrals (in Kinematics)
A mathematical tool used to find the total accumulation of a quantity over an interval, such as displacement from velocity or velocity from acceleration.
Example:
To find the total distance a rocket traveled given its velocity function, you would use an integral over the time interval.
Kinematics
The branch of mechanics that describes the motion of points, objects, and groups of objects without reference to the causes of motion.
Example:
When analyzing a car's journey, kinematics focuses on how far it traveled and how fast, not the engine's power.
Position
An object's location at a specific moment in time, often relative to a defined origin.
Example:
If you're at x = 5 meters, that's your position relative to the starting line.
Position vs. Time Graph
A graph that plots an object's position on the y-axis against time on the x-axis, where the slope represents velocity.
Example:
A straight, upward-sloping line on a position vs. time graph indicates constant positive velocity.
Scalar Quantities
Physical quantities that are fully described by only their magnitude (a numerical value) and have no direction.
Example:
The temperature outside, like 25°C, is a scalar quantity because it doesn't have a direction.
Speed
The rate at which an object covers distance over time, indicating only its magnitude. It is a scalar quantity.
Example:
A car traveling at 60 mph has a speed of 60 mph, regardless of whether it's going north or south.
Vector Quantities
Physical quantities that possess both magnitude (a numerical value) and direction.
Example:
To describe a strong wind, you need to state both its speed (magnitude) and the direction it's blowing, making it a vector quantity.
Velocity
The rate of change of an object's displacement over time, indicating both its speed and direction. It is a vector quantity.
Example:
A rocket launching upwards at 100 m/s has a positive velocity, while one descending at 50 m/s has a negative velocity.
Velocity vs. Time Graph
A graph that plots an object's velocity on the y-axis against time on the x-axis, where the slope represents acceleration and the area under the curve represents displacement.
Example:
A horizontal line on a velocity vs. time graph means the object is moving at a constant velocity (zero acceleration).