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chrisdude112
Jan27-08, 01:24 PM
1. The problem statement, all variables and given/known data
A Particle Moves along the x-axis so that its velocity v at time t \geq 0 is given by v(t)=Sin(x^{2}). The Graph of V is shown above for 0 \geq t \geq \sqrt{5\pi}. The Position of the particle at time t is x(t) and its position at time t=0 is x(0)=5

2. Relevant equations
Find the total Distance traveled b the particle from time t=0 to t=3.


3. The attempt at a solution
1. The problem statement, all variables and given/known data
We just started on integration so i figured we would need find the displacement equation by integrating the velocity equation, which would be finding:
\int Sin(x^{2} dt [0,3]. From here i have no idea how to do the equation since we're only 2 weeks into integration and have barely touched \mu Substitution

rock.freak667
Jan27-08, 01:38 PM
The only way I can see to do it is to take the taylor series of sinx and replace all the x's by x^2 and then approximate the terms.

chrisdude112
Jan27-08, 01:47 PM
oh thanks, in your opinion do you think that this problem is quite difficult for an AB AP Calculus Class?

jambaugh
Jan27-08, 02:04 PM
If the graph of the velocity is given, can you use this alone to find the distance? Remember the original definition of the integral of a function!

[also remember that as in real life, not all information available to you need be relevant.]

chrisdude112
Jan27-08, 02:12 PM
If the graph of the velocity is given, can you use this alone to find the distance? Remember the original definition of the integral of a function!

[also remember that as in real life, not all information available to you need be relevant.]

Oh. Are you referring to a of a Rieman's Sum approach to solving the equation by means of RRAM/MRAM/LRAM, Simpsons, Trapezoidal rule?