Calculating Force Using Work-Energy Relationships

[Wa1337]

Homework Statement

A body of mass 8 kg moves in a straight line on a horizontal frictionless surface. At one point in its path its speed is 4 m/s, and after it has traveled 3 m, its speed is 5 m/s in the same direction. Use work-energy relationships to find the force acting on the mass.

Homework Equations

PE = mgh
KE = 1/2mv²
ME = PE + KE

The Attempt at a Solution

Have no idea, do I calculate KE at first then at the second spot and get ΔKE or what? How do i get to finding the force with work-energy relationships?

 

[genericusrnme]

okay, you know that work = change in energy
so all you need to do is find what the change in energy is
you know how to calculate the kinetic energy KE=1/2mv^2, and you know the two values of v
so at worst you could be a factor of -1 off

once you have this value, which I'll call W, we can get to work trying to find the force (/bad pun)
you may or may not know (you should though) another way of defining work, that is

$$W=\int_{x_1}^{x_2} F dx$$

and we'll assume it's a constant force since nothing is mentioned about it varying, so solving this integral just becomes

$$W=F(x_2 - x_1)$$

which is force times the distance traveled, which you know
you should be able to work the force out from that

do you understand what I've just sad?

 

[Wa1337]

So Work = Force (Δdistance), where work is KE?