A variable force of 5x−2 pounds moves an object along a straight line when it is feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 10 ft

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pattererX · Accepted Answer

Equation #4 from this section:  If an object moves along x-axis in the positive direction from direction from x=a to x=b and f(x) is a force applied on that object.  Then the work done by this force f(x) on the object is given by  W=∫abf(x)dx  In the given case f(x)=5x−2 and [a,b]=[1,10]  Therefore  W=∫1510x−2dx    =[5x−2+1−2+1]110    =[5x−1−1]110    =[−5x]110    =[−510]−[−51]    =0.5+5=4.5lb⋅ft    Result  The work done by the given variable force on the object is 4.5lb⋅ft

A variable force of 5x^{-2} pounds moves an object along a straight line w

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