A 2 kg object is moving with a speed of 2.00 m/s in the x direction when it pass

Question

A 2 kg object is moving with a speed of 2.00 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? (Note: You will not be able to calculate the answer directly, but there is a way to estimate it!)
______J

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

(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?
_______J

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

Explanation / Answer

(a)

work done equals to area under curve

W = Area= between the x =0 to x = 2 m we have 22 square

each square area has energy 0.125 J

W =22 ( 0.125 J ) = 2.75 J

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(b)

the kinetic energy of the object at x = 2 m is

K = Ki + W = (1/2) (2) ( 2)^2 +2.75 J = 6.75 J

(c)

the speed of the object at x = 2 m is

K = 1/2 * m v^2

v = root 2K/m = root 2 (6.75)/2.0 kg = 2.59 m/s

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(d)

the work done on the object from x = 0 to x = 4 m is

W = Area= between the x =0 to x = 2 m we have 28 square

each square area has energy 0.125 J

W = 28 ( 0.125 J) = 3.5 J

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he kinetic energy of the object at x = 4 m is

K = Ki + W = (1/2) (2) ( 2)^2 +3.5= 7.5 J

v = root 2K/m = root 2 ( 7.5 J/ 2 = 2.73 m/s

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