Ogenblikkelijke versnelling

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 v_1x at time t₁. And after some time at t₂, her velocity is v_2x 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.