The force applied against an object moving horizontally on a linear path is described by #F(x)=8-x#. 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 · 2018-03-07T15:50:56

The change in kinetic energy is #=10J#

The change in kinetic energy is equal to the work done,

#DeltaKE=W#

The work done is

#dW=F(x)*dx#

#W=int_2^4(8-x)dx#

#=[8x-x^2/2]_2^4#

#=(32-8)-(16-2)#

#=24-14#

#=10J#