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**1. Homework Statement**

A particle of mass m starts from xo= 0m with vo> 0 m/s. The particle experiences the variable force Fx= Fosin(cx) as it moves to right along the x-axis, where Fo and c are constants.

a)At what position xmax does the force first reach a maximum value?

b) What is the particle's velocity as it reaches xmax? Give your answer in terms of m, vo, Fo, & c.

**2. Homework Equations**

**3. The Attempt at a Solution**

Here is my idea for part a:

Take the derivative and set it equal to 0

Fx'=Fo*c*cos(cx)

0=Fo*c*cos(cx)

cos(cx)=0

cx= pi/2

**xmax=pi/2c**Is this correct?

Then for part b:

I took the integral of Fosin(cx):

(Fo/c) * (-cos(pi/2) + 1) = Fo/c This is the work done.

Then using the work-kinetic energy theorem:

.5mvo^2 + Fo/c = .5 mv1^2 where v1 is the velocity at x max

.5vo^2 +Fo/c*m = .5v1^2

vo^2 + 2Fo/c*m = v1^2

**sqrt (vo^2 + 2Fo/c*m) = v1**