understanding physics 01: derivation of fundamental linear motion equations (cont'd)

i finally got around to doing some of the work this morning (note: since i don't know how to insert the integral symbol, i'll use an ampersand instead):

• v = dx/dt, vdt = dx, &vdt = &dx -> vt = x (assuming x0 is zero, v is avg velocity)
• a = dv/dt, adt = dv, &adt = &dv -> at + v0 = v
• distance (w/o vf): x2 - x1 = v2t - v1t, v2t = (1/2)at^2 -> x2 = x1 -v1t + (1/2)at^2
• velocity (w/o t): x = vt, v = [(v + v1)/2], t = (v - v0)/a -> x = [(v + v0)/2][(v - v0)/a] = [v^2 - (v)(v0) + (v)(v0) - v0^2]/2a = (v^2 - v0^2)/2a, 2ax = v^2 - v0^2, v^2 = v0^2 + 2ax

understanding physics 01: derivation of fundamental linear motion equations

i'm tutoring someone in physics again and i was thinking about how to explain why conservation of energy is so fundamental in physics but specifically in classical mechanics while driving to work this morning. one of the reasons i love physics more than other sciences is that it conceptual understanding doesn't require excessive blind memorization of symbols, constants, tables, taxonomic ranks, etc. If you can remember Newton's laws, understand that energy is conserved, know how work relates to force, distance and direction, you pretty much just need two equations and basic calculus to solve any problem through intermediate mechanics: F=ma and v=dx/dt. there are numerous equations you could memorize to solve problems involving linear and angular motion, but all of them are derived from v=dx/dt (i guess you also need to know that there are 2pi radians in a circle for angular motion problems). i remember that at the start of every exam, i would derive the equations for distance, velocity, acceleration and time and, for whatever reason, this would always calm me down. i've decided to see if i can still do it and will post my notes when i finish or give up

jailbreak the iphone 3GS OS 4.01

if you made the terrible, terrible mistake of upgrading your iphone 3GS to OS 4.0 before a jailbreak was released, the day of salvation has arrived. an ingenious 17 year old has released the first OTA (over the air) jailbreak for the iphone which will finally give freedom back to the poor souls on OS 4.0. backup your iphone and then open safari and navigate to http://jailbreakme.com. note that it took me three tries before the download started so don't give up if it doesn't appear to work the first time. a progress bar and status message will inform you when the download is complete and then once the jailbreak is complete and cydia is installed. if you have not already done so, allow cydia to store your ECID

jailbreak the ipad or iphone 3G/S OS 3.1.3

it is again possible to jailbreak your iphone if you made the mistake of upgrading the OS to 3.1.3 (or broke your phone and had to buy a new one that already had the damn thing on there). spirit is a small (4,464 KB), free application that jailbreaks your iphone with the click of one button in ~30 seconds including the reboot. it will also jailbreak your ipad but i won't know the amount of time that it takes until mine arrives next week :) (edit: ipad jailbreak ~15 seconds)

recommended applications once your device is free from the controlling, icy grips of apple:

• infinidock - dock as many applications as you please (well worth the $.99 cents)
• five column springboard - five columns of apps on every screen instead of four (free) (edit: note - do not install this on an ipad. it will add a fifth column but all of your icons will squish together)
• sbsettings - bossprefs 2.0. slide your finger across the top of the screen to access all of your phone information and change configure any setting you can imagine (free)
• backgrounder - run applications in the background. from experience, this is much more useful if you have a 3GS that can handle it (free)
• mxtube - save youtube videos to your phone (free)
• yourtube - like mxtube but integrated with existing youtube app ($2.00)
• lockdock - launch applications from your lock screen ($2.00)
• installous -don't feel like paying for that appstore application? get it for free using installous (free)
• appsync -include cracked applications when you backup/restore your iphone (free)

the latter two apps require you to first add the hackulo repository (from cydia: manage -> sources -> edit -> add, enter cydia.hackulo.us and click 'add source')

all thanks to @Lavarsicious for this information