Glossary
2D Kinematics
The study of motion in two dimensions, analyzing how objects move horizontally and vertically.
Example:
Understanding the flight path of a thrown football requires applying principles of 2D Kinematics to analyze its motion.
Acceleration due to gravity (g)
The constant acceleration experienced by objects near the Earth's surface due to gravitational force, approximately 9.8 m/s² directed downwards.
Example:
A dropped apple accelerates downwards at Acceleration due to gravity, increasing its speed as it falls.
Derivatives
A calculus concept used to find the instantaneous rate of change of a function, such as determining velocity from a position function.
Example:
By taking the Derivatives of a particle's position function, you can find its instantaneous velocity and acceleration at any given time.
Displacement
The overall change in an object's position from its starting point to its ending point, including both magnitude and direction.
Example:
If a runner completes a lap on a circular track, their total Displacement is zero, even though they covered a significant distance.
Fundamental Theorem of Calculus
A theorem that establishes the relationship between differentiation and integration, allowing for the calculation of net change from a rate of change.
Example:
The Fundamental Theorem of Calculus allows physicists to determine an object's change in position by integrating its velocity function over a specific time interval.
Horizontal Velocity (v_x)
The component of an object's velocity in the horizontal direction, which remains constant in projectile motion when air resistance is ignored.
Example:
When a marble rolls off a table, its Horizontal Velocity remains unchanged as it falls, even as its vertical speed increases.
Independence of Motion
The principle stating that the horizontal and vertical components of motion can be analyzed separately, with time being the common link between them.
Example:
When solving a problem involving a cannonball, you can use the Independence of Motion to calculate its horizontal range and vertical height separately.
Initial Velocity (v₀)
The velocity of an object at the moment it begins its motion or at the start of a specific observation.
Example:
The Initial Velocity of a soccer ball after being kicked determines how far and high it will travel.
Integration
A calculus concept used to find the accumulation of a quantity, such as determining displacement from a velocity function.
Example:
To calculate the total distance traveled by a rocket given its velocity function, you would perform Integration over the flight time.
Kinematic Equations
A set of mathematical equations that describe the motion of objects with constant acceleration, relating displacement, velocity, acceleration, and time.
Example:
To determine how long it takes a car to accelerate from rest to a certain speed, you would use the appropriate Kinematic Equations.
Max Height
The highest vertical position reached by a projectile during its flight, where its vertical velocity momentarily becomes zero.
Example:
A high jumper aims to achieve the greatest Max Height to clear the bar successfully without knocking it down.
Parametric Equations
Equations that describe the position (x, y) of an object as a function of time (t), allowing for analysis of its path over time.
Example:
Engineers use Parametric Equations to model the flight path of a rocket, tracking its horizontal and vertical position at every second.
Position-Time Graphs
Graphs that plot an object's position on the y-axis against time on the x-axis, where the slope represents the object's velocity.
Example:
A curved line on a Position-Time Graph indicates that an object's velocity is changing, meaning it is accelerating.
Projectile Motion
The motion of an object launched into the air, influenced solely by gravity, typically neglecting air resistance.
Example:
A diver jumping off a platform exhibits Projectile Motion as they arc through the air towards the water.
Trajectory
The curved path that a projectile follows through space.
Example:
The parabolic Trajectory of a golf ball after being hit determines where it will land on the course.
Velocity-Time Graphs
Graphs that plot 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:
The area under the curve of a Velocity-Time Graph for a car braking to a stop tells you the total distance it traveled during the braking period.
Vertical Velocity (v_y)
The component of an object's velocity in the vertical direction, which changes due to the constant acceleration of gravity.
Example:
As a thrown baseball rises, its Vertical Velocity decreases until it momentarily becomes zero at the peak of its flight.