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

[Max2020]

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

 

[BvU]

Hello @Max2020 ,

$\qquad !$​

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 ?

$\$

 

[Max2020]

Hello @Max2020 ,

$\qquad !$​

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.

 

[berkeman]

I'm sorry for posting the photo like this. I still can't see a way to resolve this issue.