Terminal speed is the constant speed reached when the resultant force in the direction of motion is zero. For a falling object, this occurs when upward fluid resistance balances the downward forces, so its acceleration becomes zero while its velocity remains non-zero.
Terminal velocity is commonly used for the corresponding signed velocity; terminal speed is the preferred wording when only the magnitude is meant.
For an object released from rest and falling through air:
- initially its speed and fluid resistance are small, so its downward acceleration is close to ;
- as speed increases, fluid resistance increases;
- the resultant downward force and acceleration magnitude decrease;
- at terminal speed the forces balance, acceleration is zero, and the object continues at constant non-zero velocity.
If a skydiver opens a parachute, the much larger effective area produces a sudden increase in drag. The acceleration is then opposite to the downward velocity, so the skydiver slows. As the speed falls, drag falls until a new balance is reached at a lower terminal speed.
For a simple falling-object model with buoyancy neglected, terminal conditions satisfy
A.1 requires qualitative fluid-resistance reasoning; a particular drag law is not required.
With downward chosen as positive:
- the - graph rises with decreasing gradient and approaches a horizontal plateau;
- the - graph decreases from near toward zero;
- the - graph begins with increasing gradient and approaches a straight line with constant non-zero gradient.
When a parachute opens, velocity remains continuous but its gradient changes sharply. The velocity then approaches a lower horizontal plateau.
With downward positive immediately after parachute opening, velocity is still positive while acceleration is negative. These opposite signs show that the skydiver is moving downward but slowing. Acceleration then approaches zero from the negative side as the lower terminal speed is established.