The only force acting on a 4.0 kg body as the body moves along an x axis varies

Question

The only force acting on a 4.0 kg body as the body moves along an x axis varies as shown in the figure. The scale of the figure's vertical axis is set by Fs = 6.0 N. The velocity of the body at x = 0 is 5.0 m/s. (a) What is the kinetic energy of the body at x = 4.0 m? (b) At what value of x will the body have a kinetic energy of 27.0 J? (c)What is the maximum kinetic energy of the body between x = 0 and x = 5.0 m?

The only force acting on a 4.0 kg body as the body moves along an x axis varies as shown in the figure. The scale of the figure's vertical axis is set by Fs = 6.0 N. The velocity of the body at x = 0 is 5.0 m/s. (a) What is the kinetic energy of the body at x = 4.0 m? (b) At what value of x will the body have a kinetic energy of 27.0 J? (c)What is the maximum kinetic energy of the body between x = 0 and x = 5.0 m?

Explanation / Answer

a)

work done by the force from t=0 to t= 4 sec is area under the curve = -12 J

so total kinetic energy = 50-12 = 38 J

b) let the time be t sec, energy by the force = 6(x-2) J

so 27= 50-6(x-2)=> x = 5.8333sec

c) max kinetic energy is at 50+(27x(2-x)/2)   for x<2mts

and if x>2 max may be 50- 27(x-2)

so max is at x=1 or max kinetic energy = 63.5 J

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