The force applied on a moving object with a mass of #7 kg # on a linear path is given by #F(x)=x #. How much work would it take to move the object over #x in [1,3] #?

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Answer 1 · 2018-03-06T01:36:52

#W = 4# J

The force function:

#F(x) = x#

Total work is force integrated through a distance:

#int_1^3F(x)dx#

#=int_1^3xdx#

#=1/2[x^2]_(1)^(3)#

#=1/2(9 - 1) = 4# J

Hence, #W = 4# J.