When will an object falling toward earth stop accelerating?

An object falling toward earth stop accelerating when it velocity becomes terminal velocity. Or When weight becomes equal to Drag force acting on the object due to air resistance.

When an object is falling towards earth, two forces act on it.

Weight ##W##due to force of gravity and is given as product of its mass and due to gravity, ##mg##. Weight acts downwards.

Drag, also called air resistance and is a type of frictional force. Drag acts opposite to the of the object. Drag equation gives the Drag Force

##F_D=1/2 rho C_D v^2 A## Where ##rho## is density of air, ##C_D## is Drag Coefficient and is a dimensionless quantity, ##v## is the velocity of object relative to air, and ##A## is the area of cross section of the object.

Now acceleration of the falling object at any given moment is given by of motion: ##F=ma##. Here ##ma=(W-F_D)## ##implies a=(W-F_D)/m## For acceleration to become zero ##(W-F_D)=0## ##impliesW=F_D##

The terminal velocity can be obtained from ##mg=1/2 rho C_D v_(termi nal)^2 A##