Find the constant c given quadratic equation F=

[rockchalk1312]

A force F=(cx-3.00x²)i acts on a particle as the particle moves along an x axis, with F in Newtons, x in meters, and c a constant. At x = 0 m, the particle's kinetic energy is 18 J; at x = 5 m, it is 12 J. Find c.

F=ma
KE=1/2mv²

I guess I don't understand the relationship between force and kinetic energy...

 

[rock.freak667]

Hint: The work done by the force is equal to the change in kinetic energy.

How is Work Done by a force defined in terms of an integral?

 

[rude man]

F = ma = dv/dt
Use chain rule to get from dv/dt to dv/dx
Come up with the differential equation relating F(x) to v and dv/dx
Solve. This results in a constant of integration plus you will still have c in the equation.
So, need 2 equations since you have 2 unknowns. Use the given boundary conditions to solve for both constants.