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

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Answer 1 · 2017-07-24T17:22:18

The change of kinetic energy is #=20.7J#

The change of kinetic energy is equal to the work.

#DeltaKE=W=F*d#

#=int_2^4(x^2-x+4)dx#

#=[x^3/3-x^2/2+4x]_2^4#

#=(64/3-8+16)-(8/3-2+8)#

#=56/3+2#

#=62/3#

#=20.7J#