When bodies fall through real fluid atmospheres, motion transitions from initial free-fall acceleration to constant terminal velocity. Analyzing the interplay between weight, air resistance, and net acceleration is essential in Cambridge IGCSE Physics.

Acceleration ($a$) is defined as the rate of change of velocity per unit time. It is a vector quantity measured in metres per second squared (m/s²).

Acceleration Equation

where $u$ is initial velocity, $v$ is final velocity, and $t$ is time. A negative value for acceleration indicates deceleration (slowing down).

Fluid Resistance and Drag

An object falling through a gas or liquid experiences an upward resistive drag force ($F_{\text{drag}}$) that opposes its downward motion. Drag force increases as the velocity of the falling object increases.

Stages of Falling Motion with Air Resistance

When a skydiver steps out of an aircraft:

1. Initial Release ($t = 0$):

• Velocity $v = 0 \implies$ Air resistance $F_{\text{drag}} = 0$.
• The only force acting is downward Weight ($W = mg$).
• Resultant force $F_{\text{net}} = W \implies$ Initial acceleration is maximum ($a = g = 9.8\text{ m/s}^2$).

1. Accelerating Phase ($v$ increases):

• As velocity increases, upward air resistance $F_{\text{drag}}$ increases.
• Net downward force decreases: $F_{\text{net}} = W - F_{\text{drag}}$.
• Acceleration decreases ($a < g$), but the speed continues to rise.

1. Terminal Velocity ($a = 0$):

• Velocity increases until upward air resistance equals downward weight ($F_{\text{drag}} = W$).
• Resultant force becomes zero ($F_{\text{net}} = 0$).
• According to Newton's First Law, acceleration ceases ($a = 0$), and the object continues falling at a constant maximum velocity called terminal velocity.

Speed-Time Curve for Terminal Velocity

On a speed-time graph for a falling object with air resistance:

• The initial gradient is steep ($g = 9.8\text{ m/s}^2$).
• The gradient curves and flattens progressively as acceleration decreases.
• The curve approaches a horizontal asymptote representing the constant terminal velocity.

Terminal velocity principles govern skydiving, meteor atmospheric entry, and raindrop falling speeds. A human falling spread-eagle reaches a terminal velocity of roughly $50\text{ m/s}$ ($180\text{ km/h}$). Opening a parachute drastically increases surface area, increasing $F_{\text{drag}}$ above $W$. This produces a net upward deceleration, rapidly lowering terminal velocity to a safe landing speed of about $5\text{ m/s}$.

Air resistance limits free-fall acceleration as falling speed rises. When upward drag balances downward weight, net force becomes zero and the body descends at constant terminal velocity.