# Question #01f3b

##### 1 Answer

#### Explanation:

Without drag, the acceleration vector is a constant vector and so the dynamics is symmetric between upward and downward motions.

But in the presence of drag, acceleration differs between the upward motion and downward motion. This is because the drag force always acts anti-parallel to the velocity vector.

**Net Force & Acceleration**:

**Upward Motion**: When the object moves upward, both gravity and drag act downward.

**Downward Motion**: When the object moves downward, gravity still acts downward but the drag force now acts upward, spoiling the symmetry.

Since the drag force acts opposite to the gravitational force during the downward motion, there is a possibility that they both might equilibrate, giving rise to a constant velocity. It is easy to calculate this **terminal velocity** and calculations look simple if we rewrite the equations in terms of this parameter

**Terminal Velocity**:

The equations (1) and (2) for the accelerations in the upward and downward directions look simple if we use the terminal velocity parameter.

Integrating acceleration once we can find the velocity as a function of time and by integrating the expression for velocity we get the position as a function of time. The following are the expressions for the velocity and positions.

**Upward Motion**: The mass

**Downward Motion**: The mass starts from a height

**Note**: Calculation details are scanned and uploaded.