ap physics unit 1 - kinematics

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

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)