Question

A variable force of 3x−2 pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 10 ft. (Round your answer to two decimal places.)

Answer 1

Answer:

$2.70J$.

Step-by-step explanation:

We have been given that a variable force of $3x^{-2}$ pounds moves an object along a straight line when it is x feet from the origin.  We are asked to find the work done in moving the object from x = 1 ft to x = 10 ft.

We know that $dW=Fdx$, where F represents force.

$dW=3x^{-2}dx$

Now, we will integrate both sides of equation as:

$\int\limits{dw} =\int\limits^{10}_1 {3x^{-2} \, dx$

Take the constant out:

$\int\limits{1dw} =3\int\limits^{10}_1 {x^{-2} \, dx$

$w =3\int\limits^{10}_1 {x^{-2} \, dx$

Upon applying power rule of integrals, we will get:

$w =3\/[ \frac{x^{-2+1}}{-2+1} ]^{10}_1$

$w =3[ \frac{x^{-1}}{-1} ]^{10}_1$

$w =3[ -\frac{1}{x} ]^{10}_1$

$w =3[ -\frac{1}{10} -(-\frac{1}{1})]$

$w =3[ -\frac{1}{10}+\frac{10}{10})]$

$w =3[\frac{9}{10}]$

$w=2.70$

Therefore, the work done by the object is $2.70J$.