Chapter 07, Problem 037- second time asking this question. Please only answer if

Question

Chapter 07, Problem 037- second time asking this question. Please only answer if you are sure

The figure gives the acceleration of a 6.0 kg particle as an applied force moves it from rest along an x axis from x = 0 to x = 9.0 m. The scale of the figure's vertical axis is set by as = 10.0 m/s2. How much work has the force done on the particle when the particle reaches (a) x = 4.0 m, (b) x = 7.0 m, and (c) x = 9.0 m? What is the particle's speed and direction (give positive answer if the particle moves along x axis in positive direction and negative otherwise) of travel when it reaches (d) x = 4.0 m, (e) x = 7.0 m, and (f) x = 9.0 m?

Explanation / Answer

(A) Work done = Mass x (Area under the a vs x curve)

= 6 ((10 x 1 / 2) + (10 x 3))

= 210 J

(b) Work done = 6 ( (10 x 1/2) + (10 x 3) + (10 x 1 / 2) - (10 x 1 / 2) - (10 x 1))

= 150 J

(c) Work done = 150 + 6(-10 x 1) + 6(-10 x 1 / 2)

= 60 J

(D) work done = change in LE

210 = 6 ( v^2 - 0)/ 2

v = 8.37 m/s

(e) 150 = 6 ( v^2 - 0^2) / 2

v = 7.07 m/s

(f) 60 = 6 v^2 / 2

v = 4.47 m/s

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