So this is a simple question that I have been confused about. Last night I was in a discussion with a friend, and we somehow ended up on this topic.
He believes that instantaneous velocity is a scalar as it has no direction.
I believe that time counts as a direction (though chances are I am wrong). So in simple velocity (lets say $m/s$) does time count as a direction?
It's a vector.
Instantaneous velocity $\vec v$ is defined as
$$\vec v \equiv \lim_{\Delta t \rightarrow 0}\frac{\Delta \vec r}{\Delta t}.$$
In that equation, $\Delta \vec r$ is the displacement that occurs during time interval $\Delta t$. Putting on my math hat for physicists, the numerator is a vector, and the denominator is a scalar, so the resulting quantity $\Delta \vec r / \Delta t$ is a vector as well. Taking the limit $\Delta t \rightarrow 0$ doesn't change the type of quantity that $\Delta \vec r / \Delta t$ is.
The fact that "time has a direction" as you pointed out is not correct in regards to what type of quantity velocity is. The vector nature comes from the $\Delta \vec r$ bit.
