Instantaneous velocity is:

Explanation

Instantaneous velocity is the velocity of an object at a specific instant in time. It is the rate of change of the object's displacement with respect to time at that precise moment. In other words, it is the slope of the object's position-time graph at a particular time point.Mathematically, the instantaneous velocity (v) of an object at time t can be expressed as the derivative of its displacement (s) with respect to time (t):v(t) = ∆s/∆twhere:v(t) = Instantaneous velocity at time t∆s = Infinitesimal change in displacement (distance traveled) during an infinitesimally short time intervaldt = Infinitesimal change in time during that same infinitesimally short time intervalIf we want to know the instantaneous velocity at a specific moment t₀, we take the limit of the average velocity over a shorter and shorter time interval Δt approaching zero:If we want to know the instantaneous velocity at a specific moment t₀, we take the limit of the average velocity over a shorter and shorter time interval Δt approaching zero:v(t₀) = lim(Δt → 0) Δs / ΔtAs the time interval Δt becomes infinitesimally small (Δt → 0), we get the instantaneous velocity at time t₀.In summary, instantaneous velocity gives us the exact velocity of an object at an exact point in time, taking into account any changes in speed and direction that may be occurring continuously during motion. It is a fundamental concept in calculus and physics, as it allows us to study the behavior of objects with precision as time changes.