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**1. Homework Statement**

An object of mass

*m*is at rest at equilibirum at the origin. At t=0, a new force [tex]\vec{F}(t)[/tex] is applied that has components

[tex]F_{x}[/tex](t) = k1+k2y [tex]F_{y}[/tex](t)=k3t

where k1, k2, and k3 are constants. Calculate the position r(t) and velocity v(t) vectors as functions of time.

**2. Homework Equations**

We know that Force = ma.

and that :

[tex]\int \vec{a}dt = \vec{v}(t)[/tex]

[tex]\int \vec{v}dt = \vec{r}(t)[/tex]

**3. The Attempt at a Solution**

I'm not sure if I'm doing this right but

I did

[tex]\vec{F}(t)[/tex] =[tex](k1+k2y)\hat{i}[/tex]+[tex](k3t)\hat{j}[/tex]

I divided the Force vector by the scalar value of m, the mass to get [tex]\vec{a}[/tex]

[tex]\vec{a}(t)[/tex] = [tex](k1+k2y)/m\hat{i}[/tex]+[tex](k3t)/m\hat{j}[/tex]

[tex]\vec{v}(t)[/tex]=[tex]\int \vec{a}dt[/tex] = [tex](k1+k2y)t/m \hat{i}[/tex] + [tex](k3t^2)/2m \hat{j}[/tex]

then integrate the velocity vector to get the position vector, am I doing this right at all?