The force applied against an object moving horizontally on a linear path is described by #F(x)=x^2+ 5 #. 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 · 2017-08-09T06:25:54

The change in kinetic energy is #=7.33J#

We need

#intx^ndx=x^(n+1)/(n+1)+C(n!=-1)#

The change in kinetic energy is equal to the work.

#DeltaW=F(x)Deltax#

Therefore,

#W=int_1^2(x^2+5)dx#

#=[x^3/3+5x]_1^2#

#=(8/3+10)-(1/3+5)#

#=5+7/3#

#=7.33J#