A 0.40kg object is projected along a frictionless straight line with a speed of 6.0m s−1 from the point x=0. In addition to its inertial motion, it is subjected to a retarding force F(x)=−4x3N that depends only on its position.
a. (i) Write an expression for the work done by the force when the object moves from x=0 to an arbitrary position x.
b. (ii) Using energy considerations, find the distance the object travels before momentarily coming to rest.