Question

a variable force of 6x−2 pounds moves an object along a straight line when it is x feet from the origin. calculate the work done (in ft-lb) in moving the object from x = 1 ft to x = 13 ft.

Answer 1

The work done in moving the object from x = 1 ft to x = 13 ft is 468 ft-lb.

Step-by-step explanation:

To calculate the work done, we can use the formula:

Work = Force x Distance

In this case, the force is given by the equation 6x - 2, and we need to find the work done in moving the object from x = 1 ft to x = 13 ft.

We can integrate the force equation over the given interval to find the work:

Work = ∫(6x - 2)dx from 1 to 13

Simplifying the integral, we get:

Work = 3x^2 - 2x

Substituting the limits of integration, we have:

Work = 3(13^2) - 2(13) - (3(1^2) - 2(1))

Solving this equation, we find that the work done in moving the object from x = 1 ft to x = 13 ft is 468 ft-lb.