The figure gives the acceleration of a 2.0 kg particle as an applied force moves

Question

The figure gives the acceleration of a 2.0 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 = 6.0 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

fro 0 to 4 m

work = w = 2(1/2*1*6+3*6) = 42 J

b) x = 7 m

w = 2(-1/2*1*6-1*6+1/2*1*6)+42 = 30 J

c) x = 9 m

w = 2(-1*6-1/2*1*6)+30 = 12 J

d) w = 1/2mv^2

v = sqrt(2*42/2) = 6.48 m/s

e) v = sqrt(2*30/2) = 5.48 m/s

f) v = sqrt(2*12/2) = 3.46 m/s

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