The force applied against an object moving horizontally on a linear path is described by #F(x)= 4x+3 N #. By how much does the object's kinetic energy change as the object moves from # x in [ 1 , 2 ]#?

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Answer 1 · 2016-05-17T09:58:55

#Delta E_k=9J#

#"Work done is equal to changing of the Kinetic Energy"#

#"Work="int _"x1"^"x2"F(x)*d x =Delta E_k#

#"Work="int_1^2(4x+3) d x=Delta E_k#

#Delta E_k=|4*x^2/2+3x|_1^2#

#Delta E_k=|2x^2+3x|_1^2#

#Delta E_k=(2*2^2+3*2)-(2*1^2+3*1)#

#Delta E_k=(8+6)-(2+3)#

#Delta E_k=14-5#

#Delta E_k=9J#