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

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Answer 1 · 2018-04-22T12:43:35

The kinetic energy changes by #=21.37J#

The change in kinetic energy is equal to the work done by the force.

#KE_2-KE_1=W#

#dW=Fdx#

#W=int_1^3(e^x+x)dx#

#=[e^x+1/2x^2]_1^3#

#=(e^3+9/2)-(e^1+1/2)#

#=e^3-e^1+4#

#=21.37J#