Acceleration of an Object in Motion and Acceleration due to Gravity

1. Any Object in Motion is said to be Accelerating if either its Speed or Direction or Both change with time. It is a Vector Quantity.
2. The Acceleration of any Object is given by the Rate of Instantaneous Change in its Velocity with respect to time. Given any Object A having a Velocity given by Vector Function \(\vec{V_A(t)}\), its Acceleration \(\vec{A_A(t)}\) is calculated as the Derivative of \(\vec{V_A(t)}\) with respect to time \(t\) as follows
   
   \(\vec{A_A(t)}={\Large \frac{d \vec{V_A(t)}}{dt}}\)   ...(1)
3. If the Direction of Acceleration of any Object changes with time whenever there is a change in its Velocity, then the Acceleration Vector can be given as a Sum of its Tangential and Normal Components. Hence, for any Object A whose Direction of Acceleration changes with time
   
   \(\vec{A_A(t)}= \vec{A_{A_T}(t)} + \vec{A_{A_N}(t)}\)   ...(2)
   
   where
   
   \(\vec{A_{A_T}(t)}\) = Tangential Component of Acceleration
   
   \(\vec{A_{A_N}(t)}\) = Normal Component of Acceleration
   
   The Tangential Component of Acceleration has the Same Direction as the Velocity of the Object.
   
   The Normal Component of Acceleration is Perpendicular to the Tangential Component in the Same Direction as the Direction of Unit Normal of the Trajectory of the Object.
4. Acceleration due to Gravity is the Rate at which every Object on or Near the Surface of Any Large Celestial Object Accelerates towards the Center of the Large Celestial Object. The Magnitude of Acceleration due to Gravity is denoted by \(g\).
   
   Magnitude of Acceleration due to Gravity \(g\) has a Constant Value of around 9.8 \({\Large \frac{m}{s^2}}\) for every Object on or Near the Surface of the Earth.