Foundations of Motion: Kinematics

Kinematics

The branch of mechanics that describes motion without regard to the forces causing it.

Scalar Quantity

A physical quantity defined by magnitude only; direction is not included.

Vector Quantity

A physical quantity defined by both magnitude and direction.

Distance

The total length of the actual path traveled; a scalar quantity.

Displacement

The straight-line change in position from the starting point to the ending point; a vector quantity.

Speed

The rate at which distance is covered.

Velocity

The rate at which displacement changes; includes direction.

Acceleration

The rate of change of velocity.

Instantaneous Velocity

The velocity at a specific moment in time.

Average Speed Equation

Average Speed = Total Distance / Time Interval.

Average Velocity Equation

Average Velocity = Displacement / Time Interval.

Position ($x$ or $v$)

The location of an object relative to a specific origin; a vector quantity.

Free Fall

A special case of 1D motion where the only force is gravity.

Acceleration due to Gravity ($g$)

A constant acceleration of approximately 9.8 m/s² acting downwards.

The Big Three (Kinematic Equations)

Equations used for constant acceleration in one-dimensional motion.

Positive Displacement

When the final position is greater than the initial position.

Negative Displacement

When the final position is less than the initial position.

Graphical Analysis

The process of interpreting motion through position, velocity, and acceleration graphs.

Position vs. Time Graph (x-t)

A graph that shows the position of an object over time; slope represents velocity.

Velocity vs. Time Graph (v-t)

A graph that shows the velocity of an object over time; slope represents acceleration.

Acceleration vs. Time Graph (a-t)

A graph that shows the acceleration of an object over time; area under the curve represents change in velocity.

Perpendicular Motions

The concept that horizontal and vertical motions in projectile motion are independent.

Decomposition of Vectors

Breaking an initial launch velocity into horizontal and vertical components.

Constant Velocity

When an object's velocity does not change over time; no acceleration.

Maximum Height in Projectile Motion

The highest point reached when vertical velocity (v_y) equals zero.

Hang Time

The total time an object spends in the air during projectile motion.

Range in Projectile Motion

The horizontal distance a projectile travels; maximum range occurs at 45 degrees on level ground.

Memory Aid for Acceleration and Velocity Interaction

If velocity and acceleration have the same sign, the object speeds up; if different, it slows down.

Odometer

An instrument that measures the distance traveled by a vehicle.

Kinematic Equations for Constant Acceleration

Equations used to model the relationship between position, velocity, acceleration, and time.

Area Under Velocity-Time Curve

Represents displacement during a time interval.

Sign Errors

Mistakes made when assigning positive or negative values to direction in motion.

Acceleration at the Peak of Trajectory

Acceleration is not zero at the peak; gravity continues to act downwards.

Stopping Distance

Distance required to stop; it quadruples if velocity doubles due to the square of the velocity term.

Vectors vs. Scalars Comparison

Vectors include both magnitude and direction; scalars include only magnitude.

Curved Line on Position vs. Time Graph

Indicates changing velocity or acceleration.

Flat Line on Position vs. Time Graph

Indicates that an object is at rest.

Steep Slope on Position vs. Time Graph

Indicates that an object is moving fast.

Vector Algebra

Involves methods such as the tail-to-tip method for adding vectors.

Distance vs. Displacement

Distance is the total path length, while displacement is the straight-line distance between two points.

Misconception about Negative Acceleration

Negative acceleration does not always mean slowing down; it depends on the direction of velocity.

Cumulative Distance

The total distance traveled being always positive.

Vector Component Equations

For projectile motion, horizontal component is constant, vertical component changes due to gravity.

Acceleration in Free Fall

Always directed downwards and equals -g.

Motion State Table

A chart that relates the signs of velocity and acceleration to the motion state.

Tail-to-Tip Method

A method used for graphically adding vectors by placing them head to tail.

Kinematic Equations Summary

A cheat sheet for solving one-dimensional motion problems with constant acceleration.