Find position (difficult).

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).

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?

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."

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.

I'll be wearing a donkey hat for the day for missing that. Well spotted.

x-3 @ room temperature ~=52 to the power ofBALROG _ COREY TAYLORS SHOE SIZE!!!!

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?