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Mirian

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a) W=2.4*1.5*cos(0)= 3.6J b) W=0.600*1.5*cos(180)= -0.9J c) W=0J because the displacement and the normal force is perpendicular to each other so cos(90)=0 d) W=0J for the same reason as part (c), but with the gravity e) W(net)= 3.6+(-0.9)+0+0= 2.7J you are
work to lift = m g h = 850 * 9.81 * 14.8 =123409.8 J/min work for Ke = (1/2)(850)(17.7)^2 =133148.25J/min C) add those and divide by 60 to get Joules/second or Watts =(123409.8+133148.25)/60=4276 J/sec or W
Take the integral of F(x) which is 18.0x-.5(.530)x^2 then plug in 12.0 for x =177.84J so .5mv^2=W since v(initial) is zero so then solve for v v(final)=((2*177.84)/8.7)^(1/2) v(final)=6.39m/s
Take the integral of F(x) which is 18.0x-.5(.530)x^2 then plug in 14.0 for x =200.06J so .5mv^2=W since v(initial) is zero so then solve for v v(final)=((2*200.06)/6)^(1/2) v(final)=8.17m/s
7.77m/s
8.04m/s

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