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Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Momentum (given mass & velocity)

Impulse/Momentum Theorem

Conservation of Momentum in an Elastic…

Conservation of Energy in an Elastic C…

P=m*v

F△t=△p

The first equation in the photo.

The second equation in the photo.

Momentum (given mass & velocity)

P=m*v

Impulse/Momentum Theorem

F△t=△p

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

A • B = ABcosθ

| A × B | = ABsinθ

v = ∆s / ∆t

v = ds / dt

write the equation for dot product... A = first vector... B = compo…

write the equation for cross product... A = first vector... B = com…

write the equation for average velocity (or speed)... v = veloci…

write the derivative for instantaneous velocity... v = instantan…

A • B = ABcosθ

write the equation for dot product... A = first vector... B = compo…

| A × B | = ABsinθ

write the equation for cross product... A = first vector... B = com…

position vs time graph

velocity vs time graph

acceleration vs time graph

in a graph always look at...

pros:... - slope = velocity... - instantaneous position... - initial p…

*most useful*... pros:... - slope = acceleration... - instantaneous v…

*relatively useless*... pros:... - slope = Jerk... - area = ∆v... cons:…

- slope... - y-intercept... - area = ∆x

position vs time graph

pros:... - slope = velocity... - instantaneous position... - initial p…

velocity vs time graph

*most useful*... pros:... - slope = acceleration... - instantaneous v…

vav = Δx / t

a = Vav / t

Vf = Vi + a * t

Δx = Vi ** t + .5 *** a * t^2

Average Velocity Equation

Average Acceleration Equation

Final Velocity Equation (given time and acceleration)

Find Displacement Equation (given time, acceleration, and ini…

vav = Δx / t

Average Velocity Equation

a = Vav / t

Average Acceleration Equation

Δx = xf - xi

Δt = tf - ti

v = Δx/Δt

xf = xi + vΔt

displacement in terms of initial and final position

time interval in terms of initial and final time

velocity in terms of displacement and time interval

final position in terms of initial position, velocity, and ti…

Δx = xf - xi

displacement in terms of initial and final position

Δt = tf - ti

time interval in terms of initial and final time

A • B = ABcosθ

| A × B | = ABsinθ

v = ∆s / ∆t

v = ds / dt

write the equation for dot product... A = first vector... B = compo…

write the equation for cross product... A = first vector... B = com…

write the equation for average velocity (or speed)... v = veloci…

write the derivative for instantaneous velocity... v = instantan…

A • B = ABcosθ

write the equation for dot product... A = first vector... B = compo…

| A × B | = ABsinθ

write the equation for cross product... A = first vector... B = com…

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Kinematics

Projectile Motion

Forces

Density

d = vt... d = [(vi + vf) ÷ 2] t... vf² = vi² + 2ad... d = vt + ½at²... vf…

y = [(viy + vfy) ÷ 2] t... vfy² = viy² + 2gy... y = vt + ½gt²... vf =…

Fnet = ma... Ff = µFn... (gravitational)... Fg = Gm₁m₂ / d²... g = GMp /…

p = mass ÷ volume

Kinematics

d = vt... d = [(vi + vf) ÷ 2] t... vf² = vi² + 2ad... d = vt + ½at²... vf…

Projectile Motion

y = [(viy + vfy) ÷ 2] t... vfy² = viy² + 2gy... y = vt + ½gt²... vf =…

NEWTONIAN MECHANICS

g = 9.8 m/s²

Δx = ½(v₀+v) ∗ t

v = v₀ + at

NEWTONIAN MECHANICS

Acceleration due to gravity on Earth

Equation for uniformly-accelerated motion that is missing the…

Equation for uniformly-accelerated motion that is missing the…

NEWTONIAN MECHANICS

NEWTONIAN MECHANICS

g = 9.8 m/s²

Acceleration due to gravity on Earth

1st kinematics equation

2nd kinematics equation

3rd kinematics equation

net force

final velocity = initial velocity + (a)(t)

delta x = (v0)(t) + 1/2 (a)(t)^2

(vf)^2 = (v0)^2 + 2(a)(delta x)

F=ma

1st kinematics equation

final velocity = initial velocity + (a)(t)

2nd kinematics equation

delta x = (v0)(t) + 1/2 (a)(t)^2

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

NEWTONIAN MECHANICS

g = 9.8 m/s²

Δx = ½(v₀+v) ∗ t

v = v₀ + at

NEWTONIAN MECHANICS

Acceleration due to gravity on Earth

Equation for uniformly-accelerated motion that is missing the…

Equation for uniformly-accelerated motion that is missing the…

NEWTONIAN MECHANICS

NEWTONIAN MECHANICS

g = 9.8 m/s²

Acceleration due to gravity on Earth

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

Definition of Average Velocity

Definition of Acceleration

Velocity of an Object as a Function of…

Displacement of an Object as a Functio…

∆x = Change in Distance... t = Elapsed Time

∆v = Change in Velocity... t = Time

v₀ = Initial Velocity... a = Acceleration... t = Time

v₀ = Initial Velocity... t = Time... a = Acceleration

Definition of Average Velocity

∆x = Change in Distance... t = Elapsed Time

Definition of Acceleration

∆v = Change in Velocity... t = Time

NEWTONIAN MECHANICS

g = 9.8 m/s²

Δx = ½(v₀+v) ∗ t

v = v₀ + at

NEWTONIAN MECHANICS

Acceleration due to gravity on Earth

Equation for uniformly-accelerated motion that is missing the…

Equation for uniformly-accelerated motion that is missing the…

NEWTONIAN MECHANICS

NEWTONIAN MECHANICS

g = 9.8 m/s²

Acceleration due to gravity on Earth

Δx = xf - xi

Δt = tf - ti

v = Δx/Δt

xf = xi + vΔt

displacement in terms of initial and final position

time interval in terms of initial and final time

velocity in terms of displacement and time interval

final position in terms of initial position, velocity, and ti…

Δx = xf - xi

displacement in terms of initial and final position

Δt = tf - ti

time interval in terms of initial and final time

Kinetic Energy

Potential Gravitational Energy

Potential Elastic Energy

Work

KE=1/2mv^2... KE=1/2{rotational inertia}{angular speed}^2

PEg=mgh... PEg=-(Gm1m2)/r

PEel=1/2kx^2

W=Fx(cos of feta)

Kinetic Energy

KE=1/2mv^2... KE=1/2{rotational inertia}{angular speed}^2

Potential Gravitational Energy

PEg=mgh... PEg=-(Gm1m2)/r