The force applied on a moving object with a mass of #2 kg # on a linear path is given by #F(x)=x^2+1 #. How much work would it take to move the object over #x in [1,4 ] #?

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Answer 1 · 2016-01-10T16:13:28

24 units

Because force is a function of #x# we write:

#W=int_1^4F.dx#

#:.W=int_1^4(x^2+1).dx#

#W=[x^3/3+x]_1^4#

#W=[64/3+4]-[1/3+1]#

#W=76/3-4/3=72/3=24"units"#

No units for distance are given. If it were metres then the answer would be in Joules.