A object is projected along a frictionless straight line with a speed of from the point

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

0.40\,\text{kg}

object is projected along a frictionless straight line with a speed of

6.0\,\text{m s}^{-1}

from the point

x=0

. In addition to its inertial motion, it is subjected to a retarding force

F(x)=-4x^{3}\,\text{N}

that depends only on its position. (i) Write an expression for the work done by the force when the object moves from

x=0

to an arbitrary position

x

. (ii) Using energy considerations, find the distance the object travels before momentarily coming to rest.