When a
particle's velocity changes, the
particle is said to undergo
acceleration (or a change in
velocity). For motion along an
axis, the
average acceleration Aavg over a
time interval t is:
Aavg = v2 - v1 / t2 - t1 = v/t
where the particle has velocity v1 at time t1 and then velocity v2 at time t2. The instantaneous acceleration (or simply acceleration) is the derivative of the velocity with respect to time.
In other words, the acceleration of a particle at any instant is the rate at which its velocity is changing at that instant. Graphically, the acceleration at any point is the slope of the curve v(t) at that point.