Spring / constant applied force question

[kennien]

Hi

A block ( 0.5 kg ) is attached to a spring ( k = 40N/m ) on a frictionless table..

The spring is 0.6 meter long unstretched ..

A constant force (20 N ) is applied horisontaly causing the spring to stretch

1) question : what is the speed/velocity of the box after 0.25 meter ?

can anyone help me with this ?

I understand that the box accelerates according to F=ma in the beginning , but when the spring starts to exert force in the other direction , that's when I am loosing it

 

[physics girl phd]

draw a free body diagram of the box when both your external force and the spring are acting on it. The diagram stays the same, even though the force of the spring changes as a function of position. Use this diagram to find F as a function of x. I'd personally approach this as a work/energy problem... using the expression for force and integrating that expression over the path of motion. then you know the energy into the system. Any energy NOT converted to potential energy in the spring remains as kinetic energy, which you can use to find speed.