Engineering Work and energy -- Change in KE due to a force F acting on a mass

AI Thread Summary
The discussion centers on the equations of motion and work-energy principles in physics. A participant points out that the force equation provided is not relevant and highlights the correct equations, including F = ma and the work done equation. There is confusion regarding the initial velocity, which is not mentioned in the calculations. The conversation also touches on a technical issue with an image that is incorrectly oriented. Overall, the focus remains on clarifying the application of the relevant physics equations.
Max2020
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Homework Statement
a force of F = 3i + (6t ^ 2) j - tk acts on a particle of mass 2 kg, where F is given in newtons and t in seconds. if the initial velocity of the particle is Vo = j + 2k, in meters per second. () What is the work done by force F during the interval 0 <= t <= 2? () Using the definition of kinetic energy (K = mv ^ 2/2), find the kinetic energy variation ∆K of the particle in the same range.
Relevant Equations
F= 3i +(6t^2) j -tk
20210426_150244.jpg
 
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Hello @Max2020 ,
:welcome: ##\qquad !##​

Did you notice your picture is rotated by 90 degrees ? It hurts to look at it !

Your $$\vec F= 3\,\hat\imath +6t^2 \,\hat\jmath -t\,\hat k $$ is not a relevant equation: it is part of the problem statement. Fortunately I do find a relevant equation (##\vec F = m\vec a##) in your picture if I almost break my neck.

The other relevant equation is ##W = \int \vec F\cdot\vec s##, also to be found in your work.

So you try to integrate ##\vec F = m\vec a\ ## twice. But I miss the given ##v_0 = \hat \jmath + 2\,\hat k\ ## there ?

Or do you have some other question that I somehow missed ?

##\ ##
 
BvU said:
Hello @Max2020 ,
:welcome: ##\qquad !##​

Did you notice your picture is rotated by 90 degrees ? It hurts to look at it !

Your $$\vec F= 3\,\hat\imath +6t^2 \,\hat\jmath -t\,\hat k $$ is not a relevant equation: it is part of the problem statement. Fortunately I do find a relevant equation (##\vec F = m\vec a##) in your picture if I almost break my neck.

The other relevant equation is ##W = \int \vec F\cdot\vec s##, also to be found in your work.

So you try to integrate ##\vec F = m\vec a\ ## twice. But I miss the given ##v_0 = \hat \jmath + 2\,\hat k\ ## there ?

Or do you have some other question that I somehow missed ?

##\ ##
I'm sorry for posting the photo like this. I still can't see a way to resolve this issue.
 
Max2020 said:
I'm sorry for posting the photo like this. I still can't see a way to resolve this issue.
1619481818607.png


:smile:
 
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