Physics Unit one

Lesson 1 — Velocity

Card 1
Front: What is the formula for average velocity?
Back: v_avg = Δx / Δt
v_avg = average velocity, Δx = displacement, Δt = change in time

Card 2
Front: What is the formula for displacement?
Back: Δx = x_f - x_i
x_f = final position, x_i = initial position

Card 3
Front: What is the formula for change in time?
Back: Δt = t_f - t_i
t_f = final time, t_i = initial time

Card 4
Front: What is the formula for speed?
Back: speed = distance / time

Card 5
Front: How are speed and velocity related?
Back: speed = |v|
Speed is the magnitude (absolute value) of velocity.

Card 6
Front: What does the slope of a position-vs-time graph represent?
Back: Velocity.
v = Δx / Δt

Lesson 2 — Acceleration

Card 7
Front: What is the formula for average acceleration?
Back: a_avg = Δv / Δt
a_avg = average acceleration, Δv = change in velocity, Δt = change in time

Card 8
Front: What is the formula for change in velocity?
Back: Δv = v_f - v_i
v_f = final velocity, v_i = initial velocity

Card 9
Front: What is the constant-acceleration velocity equation?
Back: v_f = v_i + at
v_f = final velocity, v_i = initial velocity, a = acceleration, t = time

Card 10
Front: What is the formula for change in velocity when acceleration is constant?
Back: Δv = at

Card 11
Front: What is the displacement formula for constant acceleration from rest?
Back: Δx = 1/2 at²
Δx = displacement, a = constant acceleration, t = time

Card 12
Front: What is the average velocity formula for constant acceleration?
Back: v_avg = (v_i + v_f) / 2

Card 13
Front: How do you find displacement using average velocity?
Back: Δx = v_avg t

Card 14
Front: What does the slope of a velocity-vs-time graph represent?
Back: Acceleration.
a = Δv / Δt

Card 15
Front: What does the area under a velocity-vs-time graph represent?
Back: Displacement.
Δx = area under the v-t graph

Card 16
Front: What does the area under an acceleration-vs-time graph represent?
Back: Change in velocity.
Δv = area under the a-t graph

Card 17
Front: What is the special elevator formula from the lesson?
Back: t_tot = 2√(H / a₀)
t_tot = total trip time, H = total height, a₀ = constant acceleration during the accelerating/decelerating portions

Lesson 3 — Projectile Motion

Card 18
Front: What is the horizontal position equation for projectile motion?
Back: x = x₀ + v_x t
x = horizontal position, x₀ = initial horizontal position, v_x = horizontal velocity, t = time

Card 19
Front: What happens to horizontal velocity in ideal projectile motion?
Back: v_x = constant
Horizontal acceleration is zero.

Card 20
Front: What is the vertical position equation?
Back: y = y₀ + v_y₀t + 1/2 a_y t²
y = vertical position, y₀ = initial vertical position, v_y₀ = initial vertical velocity, a_y = vertical acceleration, t = time

Card 21
Front: What is the vertical velocity equation?
Back: v_y = v_y₀ + a_y t

Card 22
Front: What is the vertical acceleration for projectile motion near Earth?
Back: a_y = -g
g = magnitude of gravitational acceleration

Card 23
Front: What is the free-fall distance equation from rest?
Back: Δy = 1/2 gt²

Card 24
Front: What is the free-fall distance equation when downward distance is positive?
Back: d = 1/2 gt²
d = distance fallen

Card 25
Front: How do you calculate the time for an object to fall from rest?
Back: t = √(2d / g)

Card 26
Front: How do you find total speed from horizontal and vertical velocity components?
Back: v = √(v_x² + v_y²)
v = total speed, v_x = horizontal velocity, v_y = vertical velocity

Card 27
Front: What is the distance between two points in 2D?
Back: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Card 28
Front: How do horizontal and vertical motion differ in projectile motion?
Back: Horizontal motion → constant velocity
Vertical motion → constant acceleration
Both use the same time t.

Lesson 4 — Energy Conservation

Card 29
Front: What is the conserved kinematics quantity introduced before energy?
Back: v² + 2gy = constant

Card 30
Front: What is the equivalent notation for the conserved kinematics quantity?
Back: v² + 2gy = c
c = constant

Card 31
Front: How do you solve the conservation equation for speed?
Back: v = √(c - 2gy)

Card 32
Front: How do you solve the conservation equation for height?
Back: y = (c - v²) / (2g)

Card 33
Front: What is the total mechanical energy equation?
Back: E = 1/2 mv² + mgy
E = total mechanical energy, m = mass, v = speed, g = gravitational acceleration, y = height

Card 34
Front: What is the formula for kinetic energy?
Back: K = 1/2 mv²

Card 35
Front: What is the formula for gravitational potential energy?
Back: U = mgy

Card 36
Front: What is the relationship between total energy, kinetic energy, and potential energy?
Back: E = K + U

Card 37
Front: What is the energy conservation equation?
Back: E_initial = E_final

Card 38
Front: What is the expanded energy conservation equation?
Back: 1/2 mv_i² + mgy_i = 1/2 mv_f² + mgy_f

Card 39
Front: What is the mass-weighted conserved quantity for multiple objects?
Back: m(v_m² + 2gy_m) + M(v_M² + 2gy_M) = constant

Card 40
Front: What is the Atwood-machine speed equation?
Back: v² = 2gH(M - m) / (M + m)
v = final speed, g = gravitational acceleration, H = distance the masses move, M = larger mass, m = smaller mass

Card 41
Front: What is the Atwood-machine acceleration equation?
Back: a = g(M - m) / (M + m)
a = acceleration, g = gravitational acceleration, M = larger mass, m = smaller mass