Q.A long stick rests on the ground, and a person stands $10\text{ m}$ away from the stick. With what minimum speed should an object of mass $0.5\text{ kg}$ be thrown along the ground so that it just reaches and hits the stick? (Assume the coefficient of kinetic friction between the object and the ground is $0.7$.)

Once an object begins sliding — i.e. once the applied force has exceeded the maximum static friction $\mu_sN$ — the opposing force from the surface is called kinetic (or sliding) friction, obeying the empirical relation $f_k=\mu_kN,$ with $\mu_k$ the coefficient of kinetic friction. Universally, $\mu_k<\mu_s$: it always takes somewhat less force to keep an object sliding than it took to start it sliding.

Comparing static and kinetic friction: static friction is a variable force, ranging from zero up to its maximum $\mu_sN$ to exactly match whatever is applied (as long as the object stays at rest); kinetic friction, once sliding starts, is essentially constant at $\mu_kN$, independent of the object's speed or of how much extra force is applied beyond what's needed to keep it moving. Both are, notably, independent of the visible area of contact — only the normal force $N$ and the nature of the two materials matter. To keep an object moving at exactly constant velocity once it is sliding, the net force must be zero, meaning the applied force must exactly balance kinetic friction — this is a common sou …