Deriving Vector and position vectors from Force vector

[HclGuy]

Homework Statement

An object of mass m is at rest at equilibirum at the origin. At t=0, a new force \vec{F}(t) is applied that has components
F_{x}(t) = k1+k2y F_{y}(t)=k3t
where k1, k2, and k3 are constants. Calculate the position r(t) and velocity v(t) vectors as functions of time.

Homework Equations

We know that Force = ma.
and that :
\int \vec{a}dt = \vec{v}(t)
\int \vec{v}dt = \vec{r}(t)

The Attempt at a Solution

I'm not sure if I'm doing this right but
I did
\vec{F}(t) =(k1+k2y)\hat{i}+(k3t)\hat{j}
I divided the Force vector by the scalar value of m, the mass to get \vec{a}
\vec{a}(t) = (k1+k2y)/m\hat{i}+(k3t)/m\hat{j}

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

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

 

[G01]

You reasoning seems good, but you are forgetting some constants when you integrate.

 

[HclGuy]

Thanks, just noticed that myself as well.

 

[SimonZ]

note that in Fx(t) = k1 + k2y, the y is not a constant, so the integral of k2y dt is not equal to k2yt