Problem 1: The acceleration of a particle varies as a function of it's position, as described in the following equation:

a = a0 * e ^ (-b * x)

Where a0 = 3 (units of m/s^2) and b = 1 (units of m^-1)

Use numerical integration to find the position and velocity of the particle at 2.37 seconds.

Edit to add: it is given that x(0) = 0 m and v(0) = 0 m/s

I get v(2.37) ~ 2.435 m/s

x(2.37) ~ 4.425 m

Problem 2: The acceleration (in m/s^2) of a particle varies with time (in s), as described in the following equation:

a = (3 + t^3) ^ 0.5

Use numerical integration to find the position and velocity of the particle at 5.7 seconds.

Edit to add: it is given that x(0) = 0 m and v(0) = 0 m/s

I get v(5.7) ~ 33.97 m/s

x(5.7) ~ 62.83 m ]]>

I have a problem with dividing tasks between people. I have 4 tasks, and somewhere between 4 and 11 people to do these tasks on a weekly basis. If there are 11 people, you can just loop through the tasks and the people, and everyone does every task the same amount of times. However, if you have 10 people and loop through the chores, every person gets the same two tasks over and over again, which is unfair. What would be the correct way of dividing the tasks for the even amount of people?

Regards,

Mindstorms ]]>

The problem I'm facing is for a spcific white pixel how to determine if it belongs or not to the hole i.e. if it's entirely surrounded by the black region.

I assume the web has a lot of related information but I just don't know what exactly to look for. Any ideas?

I'm an avid gamer and i also love thinking about how i would go about recreating real world physics withing a program or should i say how would i write it out using mathematics.......

i remember my very first physics program was making a ball bounce on screen using VB6 many years ago, it was a complete failure... it bounced but i didnt have any real knowledge back then on physics and how to apply it properly in programming...

my second project was a missile launching program, i got a map of the world off of the internet and got a scale worked out that enabled me to launch missiles to and place them using real time physics which meant i had to watch my program running for hours before a saw an explosion which was a Shape.Circle or something..... it was very satisfying to see it working after all the hard work i put behind it....

im proposing on this section that instead of having people post the problems..... lets post very simple coding examples on how to apply physics to your program, this is basically a calculus topic and its not hard to learn but its sometimes hard to make it work as i have found before that i didnt know really exactly what i need to be doing to make it work.......

some possible code examples would be....

lines (finding positions between 2 points on the line)

Slopes (finding positions between 2 points on a curve)

trajectories (with gravity, air resistance, and how the shape and composition may affect the trajectory) (just like slopes but with extra parameters)

just these 3 topics is enough to build a basic 3d graphics/gaming engine which was another project i did early on in my programming life.....

and from there like anything else the possibilities are endless..... :) ]]>