Motion Flashcards
Displacement
The change in an object’s position along a straight line, including direction (e.g., final position minus initial position).
Distance Traveled
The total length of the path an object moves along, always positive, no matter the direction.
Average Velocity
Total displacement divided by the time taken, calculated as (change in position) / (change in time).
Instantaneous Velocity
The speed and direction of an object at a specific moment, found by the rate of change of position over time.
Average Acceleration
The change in velocity divided by the time interval, calculated as (final velocity - initial velocity) / (change in time).
Instantaneous Acceleration
The rate of change of velocity at a specific moment in time.
Velocity from Position
Velocity is the derivative of position with respect to time.
Velocity from Acceleration
Velocity is the integral of acceleration with respect to time plus the initial velocity.
Acceleration from Velocity
Acceleration is the derivative of velocity with respect to time.
Position from Velocity
Position is the integral of velocity with respect to time plus the initial position.
Displacement Vector
The difference between final and initial position vectors (e.g., final position - initial position).
Position Vector
A vector showing an object’s location in 2D, with x and y components (e.g., x * i + y * j).
Average Velocity Vector
Displacement vector divided by the time interval.
Instantaneous Velocity Vector
The rate of change of the position vector with respect to time.
Average Acceleration Vector
The change in velocity vector divided by the time interval.
Instantaneous Acceleration Vector
The rate of change of the velocity vector with respect to time.
Horizontal Position in Projectile Motion
Initial horizontal velocity times time (e.g., x = v0x * t).
Vertical Position in Projectile Motion
nitial vertical velocity times time minus half of gravity times time squared (e.g., y = v0y * t - (1/2) * g * t^2).
Time of Flight for Projectile (Level Ground)
2 times initial vertical velocity divided by gravity (e.g., t = 2 * v0y / g).
Range of a Projectile (Level Ground)
(Initial velocity squared times sin of twice the angle) divided by gravity (e.g., R = (v0^2 * sin(2 * theta)) / g).
Maximum Height of a Projectile
Initial vertical velocity squared) divided by (2 times gravity) (e.g., h = (v0y^2) / (2 * g)).
Position in Circular Motion
Radius times cos(w * t) in the x-direction plus radius times sin(w * t) in the y-direction.
Angular Frequency
The rate of change of angle with respect to time, equal to tangential speed divided by radius (e.g., w = v / R).
Velocity in Circular Motion
-w times radius times sin(w * t) in the x-direction plus w times radius times cos(w * t) in the y-direction.
Period of Circular Motion
2 times pi times radius divided by tangential speed (e.g., T = 2 * pi * R / v).
Centripetal Acceleration
Tangential speed squared divided by radius, directed toward the center (e.g., a = v^2 / R).
