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 ]#?

1 Answer
Aug 9, 2017

Answer:

The change in kinetic energy is #=7.33J#

Explanation:

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#