A particle of mass m starts from x₀ = 0 m with v0 > 0 m/s. The particle experiences the variable force F_x = F₀sin(cx) as it moves to the right along the x-axis, where F₀ and c are constants.

a. What are the units of F₀ ?

b. What are the units of c ?

c. At what position x_max does the force first reach a maximum value? Your answer will be in terms of the constants F₀ and c and perhaps other numerical constants.

d. Sketch a graph of F versus x from x₀ to x_max.

e. What is the particle’s velocity as it reaches x_max? Give your answer in terms of m, v₀, F₀, and c.