Test 2 Big 5 and Freefall

displacement

△X = Xf - Xo

velocity

Vavg = △X/△t

acceleration

Aavg = △V/△t

acceleration is constant --> Ainstantaneous = Aavg

assumption when solving Big 5 equations

the 5 variables that fully describe motion

initial velocity, final velocity, acceleration, time, and displacement

Vf = Vo + at

1st equation

△X = 1/2(Vo+Vf)t

2nd equation

△X= Vot+ 1/2at²

1st quadratic

△X= Vft--1/2at²

2nd quadratic

△X = Vf²--Vo² / 2a

missing t equation

problem solving strategy

1) Read with comprehension
2) Sketch and establish coordinate system and show all vector variables (V and a only). No numbers here, only symbols
3) List all five variables. If not known, put a ?
4) Check for unit consistency (SI only), convert if necessary
5) Choose formula, quote it, and solve
6) Check answer for consistency -- sanity check

label

if a value is zero, draw this for a sketch

arrow

if a value is a vector, draw this for a sketch

two

max number of question marks in a list

free fall

motion in 1-D along a straight line under the influence of gravity only

conditions for free fall

no air resistance (or negligible), no engines (or propulsion of any kind), and no wings; all must be met

g=9.8 m/s²

all objects in free fall accelerate at the same rate of _____ (on Earth), which is due to gravity (only in NY area)

mass or shape

free fall acceleration does not depend on these two factors of the object

towards the center of the Earth

direction of free fall acceleration

g and y

a and x are replaced by these variables in vertical motion

g = --10 m/s²

used in problem solving for vertical motion; negative sign indicated the direction in our traditional coordinate system, where direction is down

constant

acceleration is __________ in freefall, so it is always equal to g no matter where it is

symmetrical

△y must equal zero for motion to be this

ratios method

allows you to solve a problem where actual values of variables (numbers) are not given; used to evaluate how a change of one variable affects another variable of interest; eliminate units, so the answer is a number

how to evaluate the results of ratios

if the ratio is >1, there is an increase
if the ratio is 1, there is no change
if the ratio is

procedure on how to use ratios

1. Find out which variable has to be evaluated
2. Find out which variable is given and will be changed
3. Examine all other variables to see is any of them are known or zero
4. Choose one of the Big 5 equations
- It has to contain the variable to be evaluated and the given one
- All other variables in the equation have to be known
5. Rearrange the equation to say eg: △y=1/2gt² if the displacement △y had to be evaluated
6. Follow one of the ratios methods: factor out method and fractions method

factor out method

Vo = zero
Vf = ?

fraction method

Vo = zero
Vf = ?

evaluate mathematical relationship between variables

Vo = zero
Vf = ?