Revise Non-uniform motion for Cambridge 9702 (3.2)

Non-uniform motion occurs whenever an object experiences a change in its velocity. This means it is either accelerating (speeding up), decelerating (slowing down), or changing its direction of travel. Crucially, a resultant (net) force must be acting on the object to cause this change; without it, velocity remains constant.

Sir Isaac Newton's three laws form the bedrock of understanding how forces cause motion. His First Law states that an object will maintain its state of rest or constant velocity unless acted upon by a resultant force. This perfectly explains why non-uniform motion requires a net force.

Newton's Second Law provides a quantitative link between force, mass, and acceleration. It tells us that the acceleration an object experiences is directly proportional to the resultant force applied to it, and inversely proportional to its mass. Crucially, both force and acceleration are vector quantities, and the direction of acceleration always matches the direction of the resultant force.

$F_{resultant} = ma$

Beyond just $F=ma$, force can also be understood in terms of momentum. Momentum ($p$) is a fundamental vector quantity that measures an object's 'quantity of motion'. It depends on both an object's mass and its velocity. The more massive or faster an object is, the greater its momentum.

$p = mv$

Newton's Third Law describes how forces always occur in pairs: 'For every action, there is an equal and opposite reaction.' When object A exerts a force on object B, object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction. These forces are critical for understanding interactions. A common point of confusion is to think these forces cancel out. They do not, because they always act on different objects and therefore cannot be combined to find a resultant force on a single object.

Weight ($W$) is the force of gravity acting on an object, pulling it towards the centre of the Earth. It's distinct from mass, which is a measure of matter. For objects near Earth's surface, we calculate weight using the object's mass and the acceleration due to gravity.

$W = mg$

When an object falls through a fluid like air, its motion is non-uniform. Initially, its weight is the dominant force, causing it to accelerate rapidly. However, as its velocity increases, resistive forces such as air resistance (drag) and upthrust begin to grow significantly.

As resistive forces increase, the resultant downward force on the falling object decreases. This, in turn, reduces its acceleration. Eventually, the upward resistive forces perfectly balance the downward driving forces (like weight). At this point, the resultant force becomes zero.

Terminal velocity is the constant, maximum velocity an object achieves when the resultant force acting on it is zero. With no net force, there is no further acceleration, and the object continues to fall at a steady speed.

The motion of a falling object can be visualised on a velocity-time graph. Initially, the gradient is steep and constant (equal to 'g' in a vacuum, slightly less in air), representing high acceleration. As speed increases, air resistance builds, so the net force and acceleration decrease, and the gradient of the graph becomes shallower. Finally, when terminal velocity is reached, the acceleration is zero, and the graph becomes a horizontal line.

For objects undergoing projectile motion, like a ball thrown through the air, air resistance has a significant effect on the trajectory. In an ideal vacuum, a projectile follows a perfectly symmetrical parabolic path. However, air resistance, a form of drag, opposes the velocity vector at all points. This continuous opposition to motion removes energy from the projectile, leading to several key differences from the ideal path.