The potential energy function for a system is given by:

u(x) = 3x^3 - 2x^2 - 6x

where x is in meters and u is in joules.
a) determine the force fx as a function of x
b) for what values of x is the force equal to zero
c) plot u(x) versus x and fx versus x, and indicate thepoints of stable and unstable equilibrium.
d) if a particle moves from x= 2m to x = 4m, find thechange in its kinetic energy. assume that the only force acting onthe particles is the force found in part (a).

What defines the mass number of an isotope? a. the sum of the neutrons and protons b. the sum of the neutrons and electrons c. the number of neutrons d. the number of protons

Acylinder with a movable piston contains 11.7 moles of a monatomic ideal gas at a pressure of 1.32×10^5 pa. the gas is initially at a temperature of 300 k. an electric heater adds 43200 j of energy into the gas while the piston moves in such a way that the pressure remains constant. cp=20.79 j k^−1 mol^−1 for a monatomic ideal gas, and that the number of gas molecules is equal to avogadro's number (6.022×10^23) times the number of moles of the gas. (a) what is the temperature of the gas after the energy is added? (b) what is the change in volume of the gas? (c) how much work is done by the gas during this process?

What is the speed of an object at a given moment?