# AP Calc Free Answer Problem:Change Over Time

1. Jan 27, 2008

### chrisdude112

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

Last edited: Jan 27, 2008
2. Jan 27, 2008

### rock.freak667

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.

3. Jan 27, 2008

### chrisdude112

oh thanks, in your opinion do you think that this problem is quite difficult for an AB AP Calculus Class?

4. Jan 27, 2008

### jambaugh

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.]

Last edited: Jan 27, 2008
5. Jan 27, 2008

### chrisdude112

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?