Terminal Velocity

This lesson covers the forces acting on falling objects and the concept of terminal velocity — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to understand how the balance between weight and air resistance changes as an object falls, and what determines the terminal velocity of different objects.

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Forces on a Falling Object

When an object falls through a fluid (such as air or water), two main forces act on it:

1. Weight (W) — the gravitational force pulling the object downward. Weight = mass × gravitational field strength (W = mg).
2. Air resistance (or drag, R) — the frictional force from the fluid acting upward, opposing the motion.

Key Points

• Weight is constant (assuming we stay near the Earth's surface where g ≈ 9.8 N/kg).
• Air resistance increases as the speed of the object increases.
• At the moment of release (from rest), air resistance is zero because the object is not yet moving.

Exam Tip: Weight does not change as an object falls (at GCSE level). Only air resistance changes — it increases with speed. This distinction is essential for explaining terminal velocity.

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The Stages of Falling

flowchart TD
    A["Object released<br/>from rest"] --> B["Stage 1: Weight >> Air Resistance<br/>Resultant force = large downward<br/>Object accelerates quickly"]
    B --> C["Stage 2: Speed increases<br/>Air resistance increases<br/>Resultant force decreases<br/>Acceleration decreases"]
    C --> D["Stage 3: Air Resistance = Weight<br/>Resultant force = 0<br/>Acceleration = 0<br/>TERMINAL VELOCITY reached"]
    D --> E["Object continues at<br/>constant speed<br/>(terminal velocity)"]

    style A fill:#2c3e50,color:#fff
    style B fill:#c0392b,color:#fff
    style C fill:#e67e22,color:#fff
    style D fill:#27ae60,color:#fff
    style E fill:#2980b9,color:#fff

Detailed Explanation of Each Stage

Stage 1: Just after release

• The object has just been released, so its speed is zero (or very low).
• Air resistance is zero (or very small) because the speed is low.
• The only significant force is weight, acting downward.
• The resultant force is large and downward → the object accelerates quickly.

Stage 2: Gaining speed

• As the object's speed increases, air resistance increases (it depends on speed).
• Weight stays the same, but the upward air resistance partially opposes it.
• The resultant downward force is smaller than before.
• The object still accelerates, but the acceleration is decreasing (the object speeds up, but more and more slowly).

Stage 3: Terminal velocity

• Eventually, air resistance grows large enough to equal the weight.
• The resultant force is zero.
• By Newton's First Law, the object continues at a constant velocity — this is the terminal velocity.
• There is no further acceleration.

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Terminal Velocity — Definition

Terminal velocity is the maximum constant velocity reached by an object falling through a fluid, when the drag force (air resistance) equals the weight of the object and the resultant force is zero.

Key Facts

• At terminal velocity, the object is not accelerating — its velocity is constant.
• The object is still moving — it has not stopped.
• Terminal velocity is reached when weight = air resistance (for a falling object).

Exam Tip: A very common exam mistake is to say that at terminal velocity "the forces are balanced so the object stops." The object does NOT stop — it continues at constant speed. Balanced forces mean no acceleration, not no movement.

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The Parachutist Example

The parachutist is the classic example used in the Edexcel specification. It involves two terminal velocities — one before the parachute opens and one after.

Stage-by-Stage Analysis

Stage	What Happens	Forces	Resultant	Velocity
1. Jumps from aircraft	Leaves the plane	W >> R (speed is low)	Large downward	Increasing rapidly
2. Falling faster	Speed builds up	W > R (R increasing)	Decreasing downward	Still increasing, but less rapidly
3. First terminal velocity	Air resistance = weight	W = R	Zero	Constant (~55 m/s)
4. Parachute opens	Large surface area suddenly increases R	R >> W	Large upward	Decreasing rapidly
5. Slowing down	Speed decreases, so R decreases	R > W (R decreasing)	Decreasing upward	Still decreasing, but less rapidly
6. Second terminal velocity	R decreases back to equal W	W = R	Zero	Constant (~5 m/s)
7. Landing	Hits the ground	Normal force acts upward	Upward (deceleration)	Reaches zero

Exam Tip: The parachutist question appears very frequently in Edexcel Physics exams. Make sure you can describe all stages, referring to the forces at each point and whether the parachutist is accelerating, decelerating or at constant velocity.

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Velocity-Time Graph for a Parachutist

The velocity-time graph for a parachutist has a distinctive shape:

1. Steep curve upward — rapid acceleration at the start.
2. Curve flattens — acceleration decreases as air resistance builds.
3. Horizontal line — first terminal velocity reached.
4. Sudden steep drop — parachute opens, rapid deceleration.
5. Curve flattens again — deceleration decreases.
6. New horizontal line — second (lower) terminal velocity reached.
7. Drop to zero — landing.

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Factors Affecting Terminal Velocity

The terminal velocity of an object depends on several factors:

Factor	Effect on Terminal Velocity	Explanation
Greater mass/weight	Higher terminal velocity	A heavier object needs more air resistance to balance its weight, which requires a higher speed
Larger surface area	Lower terminal velocity	A larger area creates more air resistance at any given speed, so balance is reached at a lower speed
Streamlined shape	Higher terminal velocity	A streamlined shape experiences less drag, so a higher speed is needed to generate enough drag
Denser fluid	Lower terminal velocity	A denser fluid (e.g. water vs air) creates more drag at any given speed

Examples