We study efficiency of intensity-based dynamic speckle method for characterization of dynamic events which occur at variable rate in time within the temporal averaging interval. We checked ability of the method to describe the speed evolution by i) numerical simulation at variable speed, ii) processing of speckle patterns obtained from phase distributions fed to a SLM at controllable change of the temporal correlation radius of speckle intensity fluctuations and iii) conducting experiments with a polymer solution drying by using a hot-stage. The numerical and SLM simulation experiments allowed for modification of the used estimates in order to obtain relevant information