3.2 Non-uniform motion

Dry friction acts at contact and is limited by μR; viscous or drag forces depend on motion through a fluid and may vary with speed, often as kv or kv² in ideal models.

Identify the regime and direction before choosing a formula. Friction can be static up to a limit, while drag is zero when relative speed is zero.

A falling object experiences weight downward and air resistance upward once it moves; a block at rest can have static friction smaller than μR.

“Resistance” is not always μR, and drag does not have a fixed value independent of speed.

For a falling object, resultant force is mg minus upward resistance. As speed grows, resistance can grow and reduce the downward acceleration.

Write m dv/dt=mg−R(v), state the drag model and use signs consistently. The no-drag constant-g solution is only an ideal comparison.

With linear drag R=kv, acceleration decreases from g at release as v increases.

Gravity does not switch off when drag appears; drag changes the resultant and therefore acceleration.

Terminal velocity is reached when acceleration becomes zero, so the upward resistive force equals the downward weight and velocity becomes constant.

Find the terminal condition from ΣF=0, not from v=0. The object may approach terminal speed asymptotically rather than reach it in finite time.

For linear resistance kv, terminal speed is mg/k; doubling mass doubles terminal speed if k is unchanged.

Terminal velocity is not the same as zero velocity, and constant velocity means zero resultant force, not zero forces.