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

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 as = 9.0 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?

The fiqure qives the acceleration of a 5.0 ky particle as an applied farce moves it frum rest along anx axis from x 0 tox-9.0 m The scale of the figure's vertical axis is set by a, -9.0 ms. How much work has the force de on the partide when the particle reaches (a) x-4.0 m, (b)x- 7.0 m, and (c) -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 otherwisa) of travel when it reaches (d)x -4.0 m, (e) x-7.0 m, and (f) x-9.0 m (a) Number (b) Number (c) Number (d) Number (e) Numbar (f) Number Units

Explanation / Answer

Work done = F*s = Area of curve*m

a)W Upto 4 m = 0.5*(4+3)*9*5 = 157.5 J (ans)

b) W upto 7m = (0.5*8*9-0.5*3*9)*5= 112.5 J (ans)

c) W upto 9 m= 0 J (ans)

d) Using energy conservation, W= 0.5mv^2

upto 4 m= 0.5*5*v^2= 157.5

V= 7.94 m/sec (ans)

e) 0.5mV1^2= 112.5

V1= 6.71 m/sec (ans)

f) 0 m/sec (ans)

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