Define the concept of instantaneous acceleration.

Instantaneous acceleration is the rate of change of velocity at a specific moment in time.

Acceleration is the rate of change of velocity, which is the rate of change of displacement. Instantaneous acceleration is the acceleration at a specific moment in time, which can be found by taking the derivative of the velocity function with respect to time.

If the velocity function is given as v(t), then the instantaneous acceleration at time t is given by a(t) = v'(t), where v'(t) is the derivative of v(t) with respect to time.

For example, if the velocity function is v(t) = 3t^2 + 2t, then the instantaneous acceleration at time t = 2 is a(2) = v'(2) = 6t + 2 = 14 m/s^2.

Instantaneous acceleration can also be found using the formula a = lim Δt→0 Δv/Δt, where Δv is the change in velocity over a small time interval Δt. This formula represents the definition of the derivative, which is the instantaneous rate of change.

In physics, instantaneous acceleration is important in understanding the motion of objects. It can be used to determine the direction and magnitude of the force acting on an object, as well as the object's position and velocity at any given time.