A constant force of 12.5 N in the positive x direction acts on an object as it moves from the origin to the point open parenthesis space 6 i with hat on top minus 8 j with hat on top space close parentheses m. How much work is done by the given force during this displacement

The work done by the given force during this displacement is 75 J.

The given parameters:

The work done by the given force during this displacement is calculated as follows;

W = F.s

W = 12.5 i . (6i - 8j)

W = (12.5 x 6)i² - (12.5 x 8)(i.j)

W = 75 - 0

W = 75 J

Thus, the work done by the given force during this displacement is 75 J.

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Explanation:

Given that

Force is acting in the positive x direction,

Then F = 12.5 •i

The displacement is given as

d = 6 •i — 8 •j

Then,

Work done?

Work done is given as the dot product of force and displacement

W = F•d

W = 12.5i •(6i — 8j)

Note that,

i•i = j•j = 1

i•j = j•i = 0

Then,

W = (12.5×6)(i•i) —(12.5×8)(i•j)

W = 75 —0

W = 75J

work is done by the given force during this displacement is 75J