 where ΔV is the difference in the velocity vector and Δ"t" is the time interval.The acceleration of the particle is the limit of the average acceleration as the time interval approaches zero, which is the time derivative,
or

Thus, acceleration is the first derivative of the velocity vector and the second derivative of the position vector of that particle.Note that in a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants.