Is acceleration a scalar or a vector quantity?

Hint: A physical quantity can either be a vector quantity or a scalar quantity. A scalar quantity is one which does not have any direction but only a magnitude. A vector quantity is one which has both direction as well as a magnitude.

Detailed step by step solution:
Some physical quantities can be completely described by just their magnitude. Such quantities are known as scalar quantities. These quantities can be added or subtracted from each other by simple rules of algebra. For example: mass of a body, speed of a body, etc.
But there are certain physical quantities which cannot be described by just their magnitude but also require some knowledge of their direction to get their complete knowledge. Such quantities are known as vectors. For example: velocity of a body, acceleration of a body, etc.
Acceleration is considered a vector quantity because it always has a certain direction. Linear acceleration of a body has direction same as that of the linear velocity of the body. The expression for acceleration is given as
$\overrightarrow a = \dfrac{{d\overrightarrow V }}{{dt}}$
This means that acceleration of a body is equal to the time rate of change of the velocity of the body. It's S.I. unit is given as metres per square seconds ($m/{s^2}$) while the C.G.S. units are centimetres per square seconds ($cm/{s^2}$)

Note: 1. The vector quantities cannot be added to each other through simple algebra but require a separate vector algebra to study their behaviour.
2. Velocity and speed are different in the sense that velocity is a scalar quantity while the magnitude of velocity gives the speed.