Non-uniform motion

Non-uniform motion occurs when an object’s velocity changes — that is, when it accelerates or decelerates. This can happen due to varying forces acting on the object, such as friction, drag, or changing applied forces.

Frictional and Drag Forces

Frictional forces act to oppose the motion of objects. There are two main types relevant here:

• Friction: Acts between solid surfaces in contact, opposing relative motion.
• Drag (Viscous) Forces: Act on objects moving through fluids (liquids or gases), such as air resistance.

Characteristics of Drag Forces

• Drag force increases as the speed of the object increases.
• At low speeds, drag may increase roughly proportionally to speed.
• At higher speeds, drag often increases with the square of speed.

Motion in a Uniform Gravitational Field with Air Resistance

When an object falls through air, two main forces act on it:

• Weight ($W = mg$), acting downwards.
• Air resistance (drag), acting upwards (opposite to motion).

At the start of the fall, air resistance is small, so the object accelerates downwards due to gravity. As speed increases, air resistance increases until it balances the weight.

Terminal Velocity

Eventually, the upward drag force equals the downward weight. The resultant force becomes zero, so the object moves at constant speed — this is called terminal velocity.

Stages of Motion (e.g., a falling object in air)

1. Initial acceleration: Only gravity acts, so object accelerates downwards.
2. Increasing speed: Air resistance grows, reducing net force and acceleration.
3. Terminal velocity: Air resistance equals weight; acceleration is zero; object falls at constant speed.

Objects Moving Against Resistive Forces

Any object moving through a fluid (air, water, oil) experiences a resistive force that increases with speed. If a constant driving force acts (e.g., a car engine or gravity), the object may reach a terminal (constant) velocity when the driving force equals the resistive force.

Summary

• Non-uniform motion involves changing velocity due to unbalanced forces.
• Friction and drag oppose motion; drag increases with speed.
• In a gravitational field with air resistance, objects accelerate until drag balances weight (terminal velocity).
• Terminal velocity is a key concept for motion with resistive forces.