Help me with these set of questions. Please do provide a complete solution to justify the answers. Thank you. 1. A factory worker pushes a 30.0-kg crate a distance of 4.5 m along a level floor at constantvelocity by pushing horizontally on it. The coefficient of kinetic friction between the crate andthe floor is 0.25. (a) What magnitude of force must the worker apply? (b) How much work isdone on the crate by this force? (c) How much work is done on the crate by friction? (d) Howmuch work is done on the crate by the normal force? By gravity? (e) What is the total workdone on the crate?2. You throw a 3.00-N rock vertically into the air from ground level. You observe that when it is15.0 m above the ground, it is traveling at 25.0 m/s upward. Use the work-energy theorem tofind (a) the rock's speed just as it left the ground and (b) its maximum height.3. A spring stores potential energy U, when it is compressed a distance xo from its uncompressedlength. (a) In terms of Uo, how much energy does the spring store when it is compressed(i) twice as much and (ii) half as much? (b) In terms of xo, how much must the spring becompressed from its uncompressed length to store (i) twice as much energy and (ii) half asmuch energy?4. A 0.65-kg ball undergoes free-fall from a height of 1.00 m above the ground. (a) Using thekinematic equation for uniformly accelerated motion, determine the speed at the given verticalpositions above the ground. (b) Find the corresponding kinetic energy, potential energy andmechanical energy for every vertical position.Position, y Speed, v, | Kinetic Energy, K | Potential Energy, U Mechanical Energy, EY1 = 1.00 mY2 = 0.75 m0.50 m%3DY3%3DY4 =0.25 mY50.00 m5. A crate on a motorized cart starts from rest and moves with a constant eastward accelerationof a = 2.80 m/s² . A worker assists the cart by pushing on the crate with a force that iseastward and has magnitude that depends on time according to F(t) =(5.40 N/s)t. What isthe instantaneous power supplied by this force at t = 5.00 s?

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