Find position (difficult).

Savielly
Posers and Puzzles 05 Nov '11 20:52
1. 05 Nov '11 20:521 edit
Over the interval 0<t<30, the velocity of a partical is given by sqrt(tan(x)).
Give an expression that gives the exact distance that the particle has traveled at time (t).
2. joe shmo
Strange Egg
05 Nov '11 21:171 edit
Originally posted by Savielly
Over the interval 0<t<30, the velocity of a partical is given by sqrt(tan(x)).
Give an expression that gives the exact distance that the particle has traveled at time (t).
are you posting your dynamics homework?

Int[x,0] (1/Sqrt(tan(x))*dx = t

good luck evaluating it!
3. 05 Nov '11 21:271 edit
Are you posting your dynamics homework?

ehm... no?

I'm aware that that's the integral...and I'm aware of how to evaluate it.
On the other hand, this forum is called "posers and puzzles."
4. joe shmo
Strange Egg
05 Nov '11 21:42
Originally posted by Savielly
Are you posting your dynamics homework?

ehm... no?

I'm aware that that's the integral...and I'm aware of how to evaluate it.
On the other hand, this forum is called "posers and puzzles."
Ok, than I bow out...because its beyond my integration skills.
5. 06 Nov '11 04:112 edits
assuming at t0, x is 0

Tan(0)=(0)

sqrt(tan(0)) = 0

velocity = 0

the particle does not move.

Therefore X at 30 = 0.

what put me onto this was that dx/dt is not a function of T and it is very sensitive to the initial value of x. As no initial value of x is given, I assume it is zero?

If X does not start at zero, we get a problem because X increases with time until it gets to x=pi/2 when tan(x) is infinite, an instant after that, tan(x) goes negative and the sqrt becomes imaginary. So, unless x is allowed to be a complex number, it pretty much has to start, and remain, at zero.
6. talzamir
Art, not a Toil
06 Nov '11 07:34
I'll be wearing a donkey hat for the day for missing that. Well spotted.
7. brang
Lone star#
07 Nov '11 17:30
x-3 @ room temperature ~=52 to the power ofBALROG _ COREY TAYLORS SHOE SIZE!!!!
8. 08 Nov '11 02:36
An interesting question is, if at Time=0 X has the value K where 0<K<pi/2, at what time does x become infinite?