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 moving the object from x = 1 ft to x = 15 ft. (Round your answer to two decimal places.)

Answer 1

644 J

Explanation:

F = 6x -2

x1 = 1 ft , x2 = 15 ft

Let dW be the small amount of work done in moving with a small distance dx.

dW = F dx

Now integrate both sides within proper limits

`\int dW = \int_(1)^(15)(6x -2)dx`

`W =[3x^(2)-2x]_(1)^(15)`

W = (3 x 225 - 2 x 15) - (3 - 2)

W = 644 J