Aparticle moving in the x direction is being acted upon by a net force f(x)=cx2, for some constant c. the particle moves from xinitial=l to xfinal=3l. what is δk, the change in kinetic energy of the particle during that time? express your answer in terms of c and l.

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.

An atom that has gained or lost electrons is called an _

Area around a charged object where the objects can exert a force on another charged objects is an electric