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SC / Physics / PHYS 201 / What are the dimensions of motion?

# What are the dimensions of motion? Description

##### Description: These notes cover all the formulas and information that should appear on the test this Monday 2/19/18.
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PHYS 201 – Dr. Wilson

## What are the dimensions of motion?

Exam 1 Study Guide

Bold = Definitions  Highlight = Formulas

Chapter 2­ Motion in One Dimension

The Basics

∙ Position(x) vs time(t) graph

o Slope = speed

∙ Displacement the change in the distance traveled/position

displacement=∆ x=x−x0

∙ Speed the amount of distance you travel in a certain amount of time (the absolute value  of the change in position over change in time) We also discuss several other topics like How does plasma membrane link adjacent cells together?

speed=|∆ x

∆t|

∙ Average Speed  the total distance, s, traveled during a particular time divided by that  time interval, t

## How are the rules of trigonometry applied?

average speed=total distance traveled

timeinterval for travel=st

∙ Constant uniform motion has a straight­line connection between position (x) and time (t)  – speed is constant

∙ Vectors  have a size(magnitude) and direction

∙ Velocity  is a vector, the quantity that describes both the direction and the speed of  motion (the change in position over the change in time)

∙ Average Velocity the displacement divided by the time elapsed during that  displacement (slope of straight line connecting the beginning and end of graph) final time−initial time=x2−x1

## What does a free-body diagram show?

If you want to learn more check out How to calculate chained or chain­weighted gdp?

velocity=⃗v=final position−initial position

t2−t1=∆ x ∆ t

∙ As we shrink our time interval, we start talking about instantaneous velocities o Instantaneous velocity the velocity at a particular point

∙ Acceleration change in motion

average acceleration=∆ v

∆t

∙ constant velocity = zero acceleration

∙ when things are increasing speed they have a positive acceleration, and when they are  decreasing speed they have a negative acceleration We also discuss several other topics like Where does acetylcholine come from?

General Equations

a=constant

∙ x0 =initial position,  v0 = initial velocity,  a = acceleration,  t = time  v=v0+at

x=x0+v0t+12at2 Don't forget about the age old question of What are examples of elementary matrices?

∙ HINT: when solving equation problems, wait as long as possible before inserting the  numbers (if you want to combine equations or solve for a specific variable)

Freefall

∙ Freefall the only force acting upon you is gravity (all objects fall at the same rate) ↓a=−9.8m/s2=−g

∙ a  is no longer unknown

v=v0−¿ If you want to learn more check out How old is the universe according to big bang theory?
Don't forget about the age old question of Why is organismal diversity study important?

y=y0+v0t−12gt2

2(−g) ( y−y0)=v2−v02

∙ Freefall graph: (will always have a curve in the negative direction)

Chapter 3­ Motion in Two Dimensions

The Basics

∙ Vector has magnitude and direction (can use an arrow to show a vector on a graph) ∙ Adding two vectors/Subtracting two vectors:

∙ Negative vector same length, opposite direction

∙ Components: a nice feature of vectors

⃗Cx,⃗Cy=components of ⃗C

length of ⃗Cx: cos30=Cx

C

length of ⃗Cy:sin 30=Cy

C

Rules of Trigonometry

SohCahToa

sinθ=opposite

hypotenuse

hypotenuse

tan θ=opposite

∙ The sides of the above triangle are all connected with trig functions ∙ Pythagorean Theorem:

Kinematics (motion) in 2­Dimmensions

average velocity∈the x−direction=v x=∆ x

∆t

average velocity∈the y−direction=vy=∆ y

∆t

average acceleration∈the x−direction=ax=∆ vx

∆t

average acceleration∈the y−direction=ay=∆ vy

∆ t

Constant Acceleration

∆ vx=v f−vi=v x−v x 0

∆ t=t−t0

ax=∆v x

∆t=vx−vx 0

∆t

∙ Projectile motion  a=g=9.81m/s2

v x=v x0+axt

x=x0+vx 0t+12axt2

v y=vy 0+a yt

y=y0+v y0t +12ayt2

2 ay ( y−y0)=v y2−vy 0

2

What Causes Motion?

∙ Velocity is motion ( ⃗v ¿

∙ Newton’s 1st Law  an object has a constant velocity unless a net force acts on it (forces  cause changes in motion)

o ex: a book will remain at rest on a table because there is no net force acting upon  it (gravity acts downward, but the table exerts an upward force of equal strength) ∙ Newton’s 2nd Law:

⃗Fnet=m a⃗

∙ Units: Newton! ( N=kg ms2)

∙ Forces can come from direct contact or action at a distance

o ex: when you drop a ball there is a net force (gravity)  ⃗Fnet=⃗Fg=m ⃗ag=mg (downward)

∙ Free­Body Diagram a picture where we attach forces to an object (vectors)

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