A object of mass 3.00 kg is subject to a force Fx that varies with position as i

Question

A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below.
this is the link to the figure
http://www.webassign.net/sercp/p5-56.gif

Find the work done by the force on the object as it moves as follows:
(a) from x = 0 to x = 4.00 m
1 J

(b) from x = 5.00 m to x = 8.00 m
2 J

(c) from x = 13.0 m to x = 15.0 m.
3 J

(d) If the object has a speed of 0.500 m/s at x = 0, find its speed at x = 5.00 m and its speed at x = 15.0 m.
speed at x = 5.00 m m/s .

speed at x = 15.0 m m/s .

Explanation / Answer

a) Work done = F.dx = area under the F-x curve

area x = 0 to 4m

tan = 3/5

W = 4 x 3 x 4 / 5x 2 = 4.8 J

b) x = 5 m to 8m

W = 3 x 3 = 9 J

c) x = 13m to 15m

W = 2 x 3 x 2 / 5 x 2 = 1.2 J

d) work- energy theorem,

W = K.E.

5 x 3/2 = 3 x v2 /2

v = 2.24 m/s

x = 5m to 15m

5 x 3 + 5 x 3/2 = 3 x ( v2 - 2.242 )/2

v = 4.47 m/s

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