Work by a linear force

A point particle of mass m=2kg is at t=0 at position x=0. It has initial velocity v₀. From t=0 to t_stop=4s it is under the influence of a force F(x) that linearly increases with the position: F(x) = k x with k>0. This is a 1D problem.

The top graph show the position of the particle. The bottom graph shows the Work done on the particle by the force and the kinetic energy of the particle.

Analyse this situation and calculate the work done by the force at any time. Is the work done in this case always sufficient to account for the change in kinetic energy?
What does it mean if the work is positive or negative?
Are the red (W) line and the green (E_kin) parallel? What does that mean?