How Do Conservative Forces Affect Potential Energy and Velocity?

[PennStateFan1]

A 29 kg object is acted on by a conservative force given by F = (-2.4)x + (-5.2)x2, with F in Newtons and x in meters. Take the potential energy associated with the force to be zero when the object is at x = 0. What is the potential energy of the system associated with the force when the object is at x = 2.0 m?


If the object has a velocity of 5.3 m/s in the negative direction of the x-axis when it is at x = 5.0 m, what is its speed when it passes through the origin?

Homework Statement

I know how to get the first part.

Homework Equations

U is the negative integral of F(x)

The Attempt at a Solution

the first part is - integral from 0 to 2 of -2.4x-5.2x^2=18.7
I don't know where to begin with the second part

 

[collinsmark]

Hello PennStateFan1,

Welcome to Physics Forum.

The object has an initial kinetic energy, at x = 5, as should be pretty easy to calculate.

Then the object picks up an additional amount of kinetic energy (going from x = 5 to x = 0) given to it by the conservative force. You should be able to figure out how much additional kinetic energy by using pretty much the same method that you used in the first part of the problem, just with different numbers, signs and such.