Pregunta: Show that if a particle experiences a force ⃗F = 2m˙s ˙ϕˆeϕ, then s =Aeϕ+Be−ϕ where A and B are constants determined from initial conditions. Hint: Note that, by the chain rule, ˙s = ˙ϕds dϕ.

To tackle this problem, we need to set up Newton's second law in polar coordinates, introduce the external force that the problem gives, and then use the given hint to develop the final motion equation.