In 1D why are vectors, such as, e.g., velocity $v$ and acceleration $a$, not written with a vector arrow? In my textbook instantaneous velocity and acceleration are wrote only as $v$ and $a$ in the chapter of One dimensional motion.
Instead, in two dimensional motion chapter they are written with the "arrow" symbol upon them, $\vec{v}$ and $\vec{a}$.
Why if they are both vectors they don't have an arrow in that particular chapter? I just can't get it.
 A: Having an arrow on top of any symbol means the quantity is a vector quantity, which has both magnitude and direction. $\vec{v}$ means the velocity vector, while $v$ Or $|\vec{v}|$ means the magnitude of the velocity vector.
In two-dimensional motion, it is mostly necessary to indicate the direction of velocity and acceleration so as to clearly specifiy the quantity. Different directions mean that the quantities cannot be just added up like in normal algebra, but requires laws of vector algebra. So, directions are of extreme necessity in 2D and 3D kinematics. Hence, the quantities are specifically indicated as vector quantities.
In one-dimensional motion, we are mostly considering motion in a straight line, so the direction is not necessary always. Only a '+' or '-' sign indicates whether the quantity is along the direction of another fixed quantity, or in an opposite direction to it.
A: In 1D we have just one direction, so it's not necessary to use an arrow to indicate it.
In 2D or 3D, we need to use an arrow because we have to specify a vector direction.
