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Graph (a) below shows the force vs. distance curve for a particle with a mass of 5kg with a speed of 7 m/s at time t=0.0s.

How fast is mass (a) moving at t=6s? in m/s

Graph (b) above shows the force vs distance curve for a particle with a mass of 4kg with an initial speed of 8m/s at time t=0.0s. How fast is mass (b) moving at t=6.0s?
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change in energy= work done= area under the graph upto 6s.

a) area=1/2*6*10 = 30

so, change in kinetic energy = 1/2*m*(vf2-vi2)

or, 30= 1/2*5*(vf2-49)

or, vf=7.81 m/s

b) area=1*10-5*3 (area below x axis does negative work and so, should be taken as negative)

or, A=-5

so, change in kinetic energy = 1/2*m*(vf2-vi2)

or, -5= 1/2*4*(vf2-64)

or, vf=7.84 m/s
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