In practice, a falling object experiences other forces besides the gravitational pull *mg*. This is especially so if the object is very light, or very bulky, or has reached sufficiently high speed such that air resistance *R* is no longer negligibly small (compared to gravitational pull).

With air resistance, the object will not be a free falling at a constant acceleration of 9.81 m s^{-2}.

Notice that while the downward weight is fixed, the upward air resistance increases with the velocity. As a result, as the object gains speed, air resistance increases continuously → net force decreases continuously → acceleration decreases continuously. At a sufficiently high speed, air resistance matches weight → net force is zero → acceleration becomes zero! The object has reached its terminal velocity!

The *a-t*, *v-t* and *s-t* graphs (↓ +ve sign convention) of such a motion are as follow:

__a-t__ graph

- The
*a-t* graph is a curve that starts at 9.81 m s^{-2} and decreases towards zero asymptotically.
- As discussed earlier, this is due to increasing air resistance causing the net force to decrease with time.
- Note that at . This is because at this instant, the object’s velocity is still zero, meaning there is no air resistance, and the resultant acceleration is
*g*.

__v-t__ graph

- the
*v-t* graph is a curve that starts from zero and increases towards the terminal velocity *v*_{t} asymptotically.
- Since the gradient of a
*v-t* graph corresponds to the acceleration, it is steepest at and becomes flatter and flatter as the acceleration decreases towards zero asymptotically.
- Note that the gradient at is equal to 9.81 m s
^{-2}. This is because at the initial point, the object’s velocity is still zero, meaning there is no air resistance, and the resultant acceleration is *g*.

__s-t__ graph

- the
*s-t* graph begins as a quadratic curve but eventually approaches a straight line.
- Since the gradient of the
*s-t* graph corresponds to the velocity, its gradient starts off completely horizontal (because ), becomes steeper and steeper as the velocity increases, but eventually stops steepening to become a straight line (because ).

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**Video Explanation **

Terminal Velocity

**Comics **

You Jump I Jump

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