Consider the motion of a 1.00-kg particle that moves with potential energy given by
U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Question

Quizplus · Accepted Answer

First, we can use conservation of energy to find the total energy of the particle at x=1.00 m:
E = K + U = (1/2)mv^2 - (2.00 J*m)/x + (4.00 J*m/(x^12)) = 1.5 J
Then, we can use conservation of energy again to find the speed at x=5.00 m:
E = (1/2)mv^2 - (2.00 J*m)/x + (4.00 J*m/(x^12)) = 1.5 J
(1/2)(1.00 kg)v^2 - (2.00 J*m)/5.00 m + (4.00 J*m/(5.00 m)^2) = 1.5 J
Solving for v, we get v = 3.67 m/s, which is choice D.

Consider the Motion of a 1