The force applied against an object moving horizontally on a linear path is described by #F(x)=x^2+ x-1 #. 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 · 2015-12-28T17:07:02

#2.5"J"#

Work done = force x distance moved in the direction of the force.

Because the force applied is a function of distance we get:

#W=int_1^2F.dx#

#:.W=int_1^2(x^2+x-1).dx#

#W=[x^3/3+x^2/2-x]_1^2#

#W=[8/3+4/2-2]-[1/3+1/2-1]#

#W=[2.66+2-2]-[1/3+1/2-1]#

#W=2.66-0.166#

#W=2.5"J"#

This work will appear as an increase in kinetic energy.