Trivial question about friction

[Telemachus]

Homework Statement

I have this doubt, I think its trivial, but I don't know how to express this thing mathematically. The thing is, I have a force F applied to an object of mas m over an horizontal path, under the action of a dynamic friction force. I know that with the force F the object will suffer an acceleration a. Let's suppose the force is F=384.16N, the mass is 98kg, the normal force is 98kg.g=960N, and the static friction coefficient is 0.4 and dynamic friction coefficient is 0.14. The object is over an horizontal surface, so the normal force is equal to the weight. The acceleration that the object will suffer due to the force is 3.92m/s^2. But the force that produces that acceleration its applied just once, so then the acceleration decays due to the dynamic friction. So I want to know how long it will take to the object to travel a distance of 10 meters. How should I proceed? should I consider an initial acceleration? how do I express the action of the dynamic friction at every instant of time?

Bye, and thanks for posting.

 

[planck42]

You use static friction to figure out if the object accelerates at all. If it doesn't, then dynamic friction is completely meaningless. If it does, then you use dynamic friction to figure out how much it accelerates. From there, you simply use those good old kinematics formulas.

 

[Telemachus]

Thanks Planck. I have just realized what I have to do. I just must consider the acceleration given by the force as an initial acceleration.

Bye there!