a = dv/dt

where:

* a is the instantaneous acceleration

* dv is the infinitesimal change in velocity

* dt is the infinitesimal change in time

This formula is derived from the definition of acceleration as the rate of change of velocity. In other words, instantaneous acceleration is the acceleration at a specific moment in time.

Here's how it works:

* Velocity is a vector quantity that describes the rate of change of position with respect to time.

* Acceleration is the rate of change of velocity with respect to time.

* Instantaneous acceleration is the acceleration at a specific point in time, which is calculated by taking the derivative of the velocity function with respect to time.

In simpler terms:

The instantaneous acceleration is the acceleration at a particular instant. To find it, you need to calculate the change in velocity over an extremely short time interval.

Example:

Imagine a car speeding up. Its velocity is changing over time. If we want to know the acceleration of the car at a specific moment, we can use the formula for instantaneous acceleration. We would measure the change in velocity over an infinitesimally small time interval, and then divide that change by the time interval. This would give us the instantaneous acceleration at that particular moment.