Help calculating work in an xy plane

[Shadow236]

Homework Statement

A force

= (1.9 N/m²)x²i is applied to a particle initially at rest in the xy plane. Find the work done by this force on the particle and the final speed of the particle as it moves along a path as follows. The given force is the only force doing work on the particle.

a) in a straight line from point (2.1 m, 2.1 m) to point (2.1 m, 7.5 m)
_________ J

b) in a straight line from point (2.1 m, 2.1 m) to point (4.8 m, 6.6 m)
__________ J

Homework Equations

W = F x d

The Attempt at a Solution

a) Due to the equation that I found above, I have used the distance formula to calculate d:
= 5.4
Then I did F x d = 1.9 * 5.4 = 10.26 (Wrong)

b) Same this as above:
= 2.7
F x d = 1.9 * 2.7 = 5.13 (Wrong)
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On top of these incorrect attempts, I am also confused with what the problem is asking... It says to find the word done by the force, and the final speed of the particle, but the answer boxes contain a J for Joules which is a unit of work. How would I put work and speed in one box?

 

[rude man]

Is the correct statement of the force F = 1.9 x² i Newtons?
(where i is the unit vector in the x direction.)

PS it does not say to find the final speed. Both answers will be in Joules.

 

[Shadow236]

Yes that is the correct statement, sorry about that. I have corrected it.

It does say in the question "Find the work done by this force on the particle and the final speed of the particle as it moves along a path as follows", but it looks like the questions are asking for work, so I guess I'll just ignore that part.

 

[haruspex]

Force and displacement are vectors. What, exactly, is the formula for the work done in terms of those vectors?

 

[Shadow236]

Oh! It looks like it's the dot product of the force and the displacement vector.

EDIT: Okay, I got a) correct: W = F dot d = 0 + 0 = 0
Now for b) I get 5.13x² and it is wrong. I think it might have something to do with the x

 

[rude man]

Oh! It looks like it's the dot product of the force and the displacement vector.

EDIT: Okay, I got a) correct: W = F dot d = 0 + 0 = 0
Now for b) I get 5.13x² and it is wrong. I think it might have something to do with the x

You have to integrate F dot dx to get part (b).