# Variable Force

1. Oct 31, 2007

### physics90604

1. The problem statement, all variables and given/known data

A particle of mass m has initial conditions x_0 = 0 m and v_0 > 0 m/s. The particle experiences the variable force F_x = F_0 sin (cx) as it moves to the right along the x-axis, where F_0 and c are constants.

What is the particle's velocity as it reaches x_max? Give your answer in terms of m, v_0, F_0, and c.

2. Relevant equations

None.

3. The attempt at a solution

Divide force by m and integrate? V_0 - (F_0 * c) / m ?

2. Oct 31, 2007

### CompuChip

You got the idea, but shouldn't the final answer depend on x_max as well?
$$\int_0^{x_0} \frac{F_0}{m} \sin(c x) = \frac{F_0}{m} \left. -cos(c x)/c \right|_{x = 0}^{x_0} = \frac{F_0}{m c} \left( 1 - \cos(c x_\text{max} \right)$$
plus v_0, or something like that (check the integration, jotted it down)