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The figure gives the acceleration of a 5.0 kg particle as an applied force moves

ID: 1639144 • Letter: T

Question

The figure gives the acceleration of a 5.0 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 a_s = 6.0 m/s^2. 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

Work done = Area under the graph*mass

a) W1 = 0.5(3+4)*6*5 = 105 J

b) W2 = 0.5(3+5)*6*5 - 0.5(2+1)*6*5 = 75 J

c) W3 = 0.5(3+5)*6*5 - 0.5(2+4)*6*5 = 30 J

velocity

v^2 = u^2 + 2ax

d) v^2 = 0 + 2*21

v = 6.48 m/s

e) v^2 = 2*15

v = 5.48 m/s

f) v^2 = 0+2*6

v = 3.46 m/s