Dynamics: (i) terminal velocity

The idea

Terminal velocity is the constant velocity reached by a falling object when the resultant force on it is zero. As an object falls through a fluid, its weight acts downwards while drag and upthrust act upwards. Drag increases with speed, so the resultant downward force decreases and acceleration falls. Eventually drag plus upthrust equals weight, the resultant force is zero, and velocity stays constant. For a skydiver, terminal velocity is reached before the parachute opens; opening the parachute increases drag, so the skydiver decelerates to a new, lower terminal velocity. The key idea is that zero resultant force means zero acceleration, not zero velocity.

What earns the marks

• Terminal velocity occurs when the resultant force on a falling object is zero.
• At terminal velocity the object moves at constant velocity, so acceleration is zero.
• Weight acts downwards; drag and upthrust act upwards through the fluid.
• Drag increases with speed until drag plus upthrust balances weight.
• A change in shape or area, such as opening a parachute, changes the terminal velocity.

Common mistakes and how to put them right

• Thinking terminal velocity means the object has stopped.

  Put it right: It is moving at constant velocity, not at rest.

• Believing acceleration is maximum at terminal velocity.

  Put it right: Acceleration is zero because the resultant force is zero.

• Ignoring upthrust and treating drag alone as balancing weight.

  Put it right: In a fluid, drag plus upthrust balances weight.

• Assuming terminal velocity is the same for all objects.

  Put it right: It depends on weight, shape and the fluid.

Exam tips

• State clearly that resultant force is zero at terminal velocity.
• Link constant velocity to zero acceleration in your explanation.
• Use a free-body diagram to show weight downwards and drag plus upthrust upwards.
• When a parachute opens, explain that increased drag causes deceleration to a lower terminal velocity.