The acceleration of an object at any given instant is called instantaneous acceleration. It is the limit of the average acceleration as the time interval approaches zero. It is the first derivative of velocity with respect to time. Consider the example of a woman walking on a road from point P1 to P2. At point P1, she has a velocity of v1x at time t1. And after some time at t2, her velocity is v2x at point P2. The change in her velocity is given by Δv in a time interval of Δt. As we consider smaller intervals of time – when the point P2 approaches P1, in the limit when Δt tends to zero, instantaneous acceleration at point P1 is given by the slope of the tangent to the curve at point P1. Lastly, the instantaneous acceleration of a body can also be calculated as the second derivative of the position with respect to time using the position versus time graph.