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

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The discussion focuses on solving force graph problems related to work, kinetic energy, and speed calculations for a 4 kg object moving at 2.10 m/s. The key tasks include calculating the work done by a variable force Fx from x = 0 to x = 2 m, determining the kinetic energy at x = 2 m, and finding the object's speed at both x = 2 m and x = 4 m. The integration of the force function over the specified distance is essential for determining the work done, which is critical for solving the kinetic energy and speed questions.

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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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