thanks Doc Al. I did this, dividing the three regions of the velocity graph and calculated the area beneath each of those regions. I came up with 215 meters but the online assignment checker counted it as wrong so I am a little confused.
I can't for the life of me figure this out. The question is, based on this graph, determine the total distance the particle traveled during the first 20 seconds.
http://seminario.no-ip.com/graph.gif
I graphed the velocity graph just fine based on the acceleration graph. but the position...
I have to integrate:
sqrt( (3t^2)^2 + (1)^2 + (sqrt(6)t)^2 ) at the limits t=1 and t=3
I can't figure out how to simplify the problem so that I can do the integral.
So far the farthest I've gotten is the obvious:
sqrt( 9t^4 + 6t^2 + 1 )
now I am stuck.
can i ask what programs you guys use to write out your mathematical formulas? i realize they are images.. so you must be making them some where.
edit: by the way, thanks chen
question, i understand the way you worked this, however, why would i have to calculate the velocities separately for each axis?
wouldnt the position vector be r(t) = acos(wt)i + asin(wt)j + btk ?
then i would just do dr/dt to find the velocity vector wouldn't i? and dv/dt to find the...
thanks. I'm aware of how to obtain the velocity, speed and acceleration vectors, however I just didnt know why he would include a,b,w. doesn't make much sense to me.
http://seminario.no-ip.com/problem2.gif
I'm confused about the above problem because I don't know why there would be an a,b, or greek letter "w" in there. Anyone?
i know what youre hinting at that i could divide both sides of the equation by 2 and then sub x and y for r cos(theta) and r sin(theta) and then cancel the r^2 on both sides and have sin(2theta) left.. but that would leave me with
(z^2 cos(2theta)) / 2 = sin(2theta) is that correct though...