The figure gives the acceleration of a 3.0 kg particle as an applied force moves

Question

The figure gives the acceleration of a 3.0 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 = 8.0 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

Work done by the variable force = area under the curve

a) x = 4 m

then W1 = ((4-1)*8) +(0.5*1*8) = 28 J

b) x = 7 m

W2 = W1+(0.5*1*8)-(0.5*1*8) = W1 = 28 J

c) x= 9 m

W = W2-(0.5*1*8)-(2*8)-(0.5*1*8) = 4 J

d) x = 4 m

Using work energy theorem

W1 = 0.5*m*v^2

28 = 0.5*3*v^2

v = 4.32 m/sec

e) x = 7 m

W2 = 0.5*m*v^2

28 = 0.5*3*v^2

v = 4.32 m/sec

f) x = 9 m

W = 0.5*m*v^2

4 = 0.5*3*v^2

v = 1.64 m/sec

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