Solving Force Graph Problems: Work, Kinetic Energy, and Speed Calculations

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The discussion revolves around calculating work, kinetic energy, and speed for a 4 kg object influenced by a variable force as it moves along the x-axis. Participants emphasize the need to integrate the force function over the specified distance to determine the work done. The kinetic energy at different positions is also a focal point, requiring the application of the work-energy principle. Additionally, the speed of the object at various points is sought, linking back to the calculated work and kinetic energy. Clarification on the force function to be integrated is requested to initiate the calculations.
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Here is the diagram.
337713766.jpg


A 4 kg object is moving with a speed of 2.10 m/s in the x direction when it passes the origin, as shown in the figure below. It is acted on by a single force Fx that varies with x.
(a) What is the work done by the force from x = 0 to x = 2 m?

b) What is the kinetic energy of the object at x = 2 m?

(c) What is the speed of the object at x = 2 m?
m/s

(d) What is the work done on the object from x = 0 to x = 4 m?

(e) What is the speed of the object at x = 4 m?

I know I have to integrate to get the work done.
It is the integral from point x1 to point x2 of Fx Dx
My question is, what do I integrate?

Can someone help me get started? Thanks.
 
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Anyone help me get started?
 

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