Terminal velocity (AQA GCSE Physics): Revision Notes
Terminal velocity
What is terminal velocity?
When objects fall towards Earth, they don't keep speeding up forever. Terminal velocity is the constant speed an object reaches when it has been falling for long enough.
At terminal velocity, the object stops accelerating and falls at a steady speed.
This constant speed is reached when the forces acting on the falling object become balanced, creating a state of equilibrium during the fall.
Free fall and reaching terminal velocity
When an object first starts falling, it's in free fall. This means gravity is pulling it down and making it speed up.
Near Earth's surface, objects accelerate at 9.8 m/s² due to gravity.
The acceleration due to gravity () is constant near Earth's surface, regardless of the object's mass. This is a fundamental principle that applies to all falling objects in the absence of air resistance.
The three stages of falling
Stage 1: Object starts falling
- Weight pulls the object down
- Very little air resistance at first
- Object accelerates quickly downwards
Stage 2: Speed increases
- As the object falls faster, air resistance gets stronger
- Weight is still greater than air resistance
- Object still accelerates, but more slowly
Stage 3: Terminal velocity reached
- Air resistance equals the object's weight
- The forces are balanced (resultant force = zero)
- Object falls at constant speed - this is terminal velocity
Understanding velocity-time graphs
A velocity-time graph shows how terminal velocity works by displaying the relationship between speed and time during the fall:
Section AB: Small air resistance, large resultant force downwards. Object accelerates quickly.
Section BC: Air resistance increases as speed increases. Acceleration gets smaller.
Section CD: Air resistance equals weight. No acceleration - terminal velocity reached.
Section DE: If a parachute opens, air resistance becomes much bigger than weight. Object slows down.
Section EF: Forces balance again at a new, slower terminal velocity.
The velocity-time graph for terminal velocity typically shows a curved line that starts steep and gradually levels off to become horizontal, representing the transition from acceleration to constant velocity.
Key factors affecting terminal velocity
- Shape and size: Larger surface area = more air resistance = lower terminal velocity
- Weight: Heavier objects have higher terminal velocity
- Medium: Falling through water or thick liquid gives lower terminal velocity than air
These factors work together to determine the final terminal velocity. An object's terminal velocity is not fixed - it depends on both the object's properties and the medium it's falling through.
Example: Ball in thick liquid
Worked Example: Ball Falling Through Thick Liquid
When a ball falls through thick liquid:
Step 1: Initial motion
- Ball accelerates at first due to gravitational force
Step 2: Increasing resistance
- Resistance increases as speed increases due to the viscosity of the liquid
Step 3: Equilibrium reached
- Eventually reaches terminal velocity when gravitational force equals drag force
Result: The velocity-time graph shows velocity increasing rapidly at first, then gradually levelling off to a constant value.
Key takeaways
Key Points to Remember:
- Terminal velocity happens when air resistance equals weight
- Objects accelerate when they first start falling at
- Forces balance at terminal velocity, so there's no more acceleration
- Bigger surface area means lower terminal velocity
- Heavier objects have higher terminal velocity in the same medium