AP PHYSICS unit 1

What is a scalar?

Magnitude

What are some examples of scalar?

time, distance, speed, mass

What is a vector?

Magnitude and direction

What are some examples of a vector?

displacement, velocity, acceleration

The difference between Speed and velocity?

Speed = how fast. Velocity = speed with direction

The difference between displacement and distance?

Distance = total path. Displacement = final position − initial position

What is vector magnitude?

A vector’s size or length

How do you find vector components?

If θ is measured from horizontal: Aₓ = A cos θ; Aᵧ = A sin θ

When do sine and cosine switch roles?

When the angle is measured from the vertical instead of horizontal

How do you find a vector’s magnitude from its components?

A = √(Aₓ² + Aᵧ²)

How do you find a vector’s direction?

θ = tan⁻¹(Aᵧ/Aₓ); check the quadrant

What are unit vectors i, j, and k?

Magnitude-1 vectors along the x-, y-, and z-axes

How do you write a 2D vector

A = Aₓi + Aᵧj

How do you find a 3D vector’s magnitude?

|A| = √(Aₓ² + Aᵧ² + A_z²)

What is position?

An object’s location relative to an origin

What is displacement?

Δx = x_f − x_i

What does Δ mean?

“Change in,” such as Δv = change in velocity

Can displacement be negative?

Yes. It indicates displacement in the negative direction

Can displacement be zero while distance is not?

Yes. An object can return to its starting point

How do distance and displacement magnitude compare?

Distance ≥ |displacement|

Move 8 m east, then 3 m west. Distance and displacement?

Distance = 11 m; displacement = 5 m east

Position vs. displacement?

Position = location; displacement = change in location

Average velocity formula

v_avg = Δx/Δt

Average speed?

Total distance ÷ total time

Why can average speed differ from average velocity’s magnitude

Distance and displacement can differ

Instantaneous velocity?

v = dx/dt; the derivative of position

What does velocity’s sign tell you?

Direction along your chosen axis

Can velocity be negative while speed is positive?

Yes. Speed = |velocity|