Question about notation in physics

[monac]

So it says that a particle is going with a velocity of 5i m/s at t = 0 and varying acceleration a = 6√t j.
it asked me to find the velocity and position of the particle as a function of time.
So i did an integral of the acceleration to get velocity and did the integral of the velocity to get the position. I was wondering whenever i write the equation as a function of time, do i still need that arrow (→ ) on top of the v for vector and r for position?

 

[SammyS]

So it says that a particle is going with a velocity of 5i m/s at t = 0 and varying acceleration a = 6√t j.
it asked me to find the velocity and position of the particle as a function of time.
So i did an integral of the acceleration to get velocity and did the integral of the velocity to get the position. I was wondering whenever i write the equation as a function of time, do i still need that arrow (→ ) on top of the v for vector and r for position?

If it's a vector, then yes, we usually put the arrow above the variable.

$\vec{r}(t) = x(t)\hat{i}+t(t)\hat{j}+z(t)\hat{k}$

 

[monac]

If it's a vector, then yes, we usually put the arrow above the variable.

$\vec{r}(t) = x(t)\hat{i}+t(t)\hat{j}+z(t)\hat{k}$

so if I solved the integral and I got like
r(t) = 8t^2 + 5t
I put the arrow on top of the arrow since it's a vector. I get that ...
But do I still include the i and j?
so would it be r(t) = 8t^2 i + 5t j ?

 

[SammyS]

so if I solved the integral and I got like
r(t) = 8t^2 + 5t
I put the arrow on top of the arrow since it's a vector. I get that ...
But do I still include the i and j?
so would it be r(t) = 8t^2 i + 5t j ?

Yes, use the $\hat{i}$ & $\hat{j}\,.$

If the left side of an equation is a vector, then the right side must also be a vector.

 

[monac]

Thank you! :)