Glossary
Acceleration
The rate at which an object's velocity changes, which can involve a change in speed, direction, or both.
Example:
A satellite in a circular orbit around Earth is constantly undergoing acceleration because its direction of motion is always changing, even if its speed is constant.
Acceleration Conditions
Acceleration occurs whenever an object's velocity changes, which can be due to a change in speed (magnitude) or a change in direction, or both.
Example:
A car speeding up, slowing down, or turning a corner are all examples of situations where acceleration conditions are met.
Average Acceleration
The rate at which an object's velocity changes over a specific time interval. It is calculated by dividing the change in velocity by the time taken.
Example:
A rocket launching from rest that reaches 50 m/s in 5 seconds has an average acceleration of 10 m/s².
Average Acceleration
The total change in an object's velocity divided by the total time interval over which that change occurred.
Example:
If a braking car's velocity changes from 30 m/s to 10 m/s in 4 seconds, its average acceleration is -5 m/s² (indicating deceleration).
Average Velocity
The rate at which an object's displacement changes over a specific time interval. It is calculated by dividing the total displacement by the total time taken.
Example:
A car that travels 100 meters north in 20 seconds has an average velocity of 5 m/s north.
Average Velocity
The total displacement of an object divided by the total time interval over which that displacement occurred.
Example:
A car that travels 200 meters north in 20 seconds has an average velocity of 10 m/s north, regardless of any stops or turns it made during the trip.
Calculus in Kinematics
The application of differentiation and integration to analyze motion, allowing for the determination of instantaneous values and relationships between position, velocity, and acceleration when they are not constant.
Example:
Understanding calculus in kinematics allows you to solve complex problems where acceleration changes over time, such as finding the maximum height of a projectile with air resistance.
Charge
An intrinsic property of matter that causes it to experience a force when placed in an electromagnetic field.
Example:
An electron carries a fundamental negative charge, which dictates its interaction with electric fields.
Differentiation
A calculus operation used to find the rate of change of a function, such as determining velocity from a position function.
Example:
To find the instantaneous velocity of a particle whose position is described by x(t) = 4t³ - 2t, you would perform differentiation of x(t) with respect to time.
Direction
The orientation or path along which a vector quantity (like displacement, velocity, or acceleration) is acting. It is typically indicated by positive/negative signs or compass directions.
Example:
When a ball is thrown upwards, its velocity has an upward direction, but its acceleration due to gravity has a downward direction.
Displacement
The change in an object's position, calculated as the final position minus the initial position. It is a vector quantity, meaning it has both magnitude and direction.
Example:
If you walk 5 meters east and then 5 meters west, your total displacement is 0 meters, even though you walked a total distance of 10 meters.
Displacement
The vector quantity representing the change in an object's position, measured as the straight-line distance and direction from its initial to its final point.
Example:
If a squirrel runs 10 meters up a tree and then 10 meters back down to its starting branch, its total distance traveled is 20 meters, but its displacement is zero.
Graphical Analysis
The interpretation of motion by examining position-time, velocity-time, and acceleration-time graphs to extract information about an object's movement.
Example:
From a velocity-time graph, the slope represents acceleration and the area under the curve represents displacement, which are key aspects of graphical analysis.
Instantaneous Acceleration
The acceleration of an object at a specific moment in time, given by the derivative of its velocity function with respect to time.
Example:
If a car's velocity is described by v(t) = 6t² - 2t, its instantaneous acceleration at t=3 seconds is 34 m/s².
Instantaneous Values
The precise value of a physical quantity, such as velocity or acceleration, at a specific moment in time, found by taking the limit as the time interval approaches zero.
Example:
While driving, the reading on your car's speedometer gives you the instantaneous values of your speed at that exact moment.
Instantaneous Velocity
The velocity of an object at a specific moment in time, given by the derivative of its position function with respect to time.
Example:
If a particle's position is given by x(t) = 5t² + 3, its instantaneous velocity at t=1 second is 10 m/s.
Instantaneous vs. Average Values
Average values describe motion over a time interval, while instantaneous values describe motion at a specific moment in time. Average values approximate instantaneous values as the time interval approaches zero.
Example:
Your car's speedometer shows your instantaneous speed, whereas calculating your total trip distance divided by total time gives your average speed.
Integration
A calculus operation used to find the accumulation of a quantity, such as determining velocity from an acceleration function or position from a velocity function.
Example:
To find the total displacement of a rocket given its velocity function v(t) over a certain time, you would perform integration of v(t) with respect to time.
Kinematic Equations
A set of mathematical formulas that describe the motion of objects with constant acceleration. These equations relate displacement, initial velocity, final velocity, acceleration, and time.
Example:
To predict how far a dropped object will fall in a certain amount of time, you would use the kinematic equations.
Kinematics Equations
A set of mathematical formulas that relate displacement, velocity, acceleration, and time for objects undergoing constant acceleration.
Example:
Using the kinematics equations, you can quickly calculate how far a car travels if it accelerates uniformly from rest for 5 seconds at 2 m/s².
Limit
A mathematical concept in calculus describing the value that a function approaches as its input approaches a certain value.
Example:
The concept of a limit is crucial for defining instantaneous velocity as the displacement over an infinitesimally small time interval.
Mass
A fundamental property of matter that quantifies its inertia, representing its resistance to changes in motion.
Example:
A loaded freight train has an enormous mass, which is why it takes a very long time to speed up or slow down.
Object Model Simplification
A method in physics where an object's size, shape, and internal configuration are ignored, treating it as a single point with properties like mass and charge.
Example:
When analyzing the trajectory of a thrown baseball, we often treat it as a point mass to simplify calculations, ignoring its spin or exact dimensions.
Point Particles
A simplified model where an object's size and shape are ignored, treating it as a single point in space for motion analysis.
Example:
When analyzing the trajectory of a thrown football, physicists often treat it as a point particle to simplify calculations, ignoring its rotation or air resistance effects.
Time Interval
The duration between two specific moments in time, over which changes in physical quantities are measured.
Example:
To calculate the average speed of a sprinter, you measure the total distance they ran and divide it by the time interval from start to finish.
Time-Dependent Functions
Mathematical expressions that describe how physical quantities like position, velocity, or acceleration change over time.
Example:
The equation v(t) = 9.8t represents the time-dependent function for the velocity of an object in free fall, assuming it starts from rest.
Units
Standardized measurements used to quantify physical quantities. Always including correct units in answers is crucial for clarity and correctness in physics.
Example:
When stating a car's speed, always include units like 'm/s' or 'km/h' to specify what the numerical value represents.
Vector Quantity
A physical quantity that possesses both magnitude (size) and direction.
Example:
To fully describe the velocity of a spaceship, you need to state both its speed (magnitude) and its direction of travel, making velocity a vector quantity.