Live cell imaging is a powerful tool to understand how nano-sized objects, such as the drug carriers used for nanomedicine applications, are taken up and trafficked by cells. Here we visualized human HeLa cells as they took up and trafficked nanoparticles of different sizes and quantified nanoparticle colocalization with different fluorescently-labelled intracellular compartments over time. This allowed us to obtain kinetic profiles of nanoparticle transport towards the lysosomes in individual cells. With a simple theoretical model, we determined the typical departure time of nanoparticles from the cell membrane and typical lysosome arrival time. We compared these kinetics parameters for nanoparticles of different sizes and determined how they vary in individual cells. We also performed a similar analysis for early endocytic compartments through which nanoparticles transit and discuss challenges in quantifying the colocalization in this case. The results show a high variability in intracellular trafficking kinetics between individual cells. Additionally, they help us to understand how nanoparticle properties affect their cellular uptake and intracellular distribution kinetics.