note for non-phs students: this is based on phs' ap physics curriculum (guided notes and stuff) and the openstax textbook :) but it could still give broad vocab and concepts on kinematics!!
Vector
A quantity with direction and magnitude
Scalar
A quantity with magnitude
Velocity (m/s)
The rate of change in position (specifically displacement) and is a vector
In a velocity vs. time graph, the slope is the acceleration and the area is the displacement
Average velocity can be calculated from the change in position (xᶠ-x⁰)/change in time
Instantaneous velocity is the slope at one point in the graph
Acceleration of gravity
9.81 or 10 m/s²
Distance (m)
The magnitude between two positions and is scalar
We can calculate the distance with the absolute value difference between positions and add it all up
Displacement (m)
The change in a position of an object
We can calculate the displacement with xᶠ-x⁰
In a position vs. time graph, the slope is the velocity
Motion maps
Bigger arrow size = Fast and vice versa
Small distance between arrows = Fast speed and/or velocity and vice versa
Same distance between arrows = Constant speed and/or velocity
Relative velocity
The velocity of one body with respect to another body
What does it mean for velocity and acceleration to have the same sign?
It is speeding up
What does it mean for velocity and acceleration to have the opposite sign?
It is slowing down
Could we have zero velocity and non-zero acceleration?
Yes, this happens when an object is in the process of changing its speed or direction, even if it’s not moving. An example is when a car is coming to a stop while braking, it is undergoing negative acceleration but has zero velocity
Could we have non-zero velocity and zero acceleration?
Yes, it is when we have a constant velocity. This means an object is steadily moving with no change in speed or direction
Could we have negative velocity and positive position?
Yes, the object would be moving backward (- velocity) while still being located ahead (+ position) of it’s starting point
Acceleration (m/s²)
The rate at which velocity is changing
In an acceleration vs. time graph, the area is the velocity. Usually, it is the area of a triangle (½b x h), square (l x w), or both (do both separately and then add together)
One-dimensional kinematic equations
No position or distance: v = v⁰ + at
No final velocity: x = x⁰ + v⁰t + ½at²
No time: v² = (v⁰)² + 2a (x-x⁰)
Variables for one-dimensional kinematic equations
xⁱ or x⁰ = initial position in m, xᶠ= final position in m, vⁱ or v⁰ = initial velocity in m/s, vᶠ= final velocity in m/s, a = acceleration in m/s², t = time
An object in free-fall is moving under the influence of only _
Gravity
This means air resistance acting on an object is not free-fall
Gravity and free-fall equations
In these equations, the position variable is y (not x)
No position or distance: v = vⁱ + at
No final velocity: y = y⁰ + v⁰t + ½at²
No time: v² = (v⁰)² + 2a (y-y⁰)
Horizontal Component of Vector V
Vx = vcosθ
Vertical Component of Vector V
Vy = vsinθ
Horizontal Motion Equation
x = x⁰ + v⁰t
Magnitude of Vector V
V = √(Vx² + Vy²)
Direction of Vector V
θ = tan-1(Vy/Vx)