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Determining the vehicle excise tax in Massachusetts involves a straightforward process. The state levies a 6.25% sales tax on the purchase price of a vehicle. For example, if a car costs $20,000, the sales tax would be $1,250. This amount is added to the purchase price and paid at the time of registration. In addition to the sales tax, municipalities also levy an annual excise tax based on the vehicle’s value.

Accurate computation of this tax is crucial for both buyers and sellers. Understanding the total cost of vehicle ownership, including taxes, allows buyers to budget effectively. For sellers, providing clear and accurate tax information can facilitate smoother transactions. Historically, sales tax has been a significant revenue source for state governments, funding essential public services like infrastructure and education. The implementation of a statewide sales tax on vehicles ensures a consistent and predictable revenue stream for the Commonwealth.

Determining mean squared displacement involves analyzing the average change in position of particles or objects over time. A practical example involves tracking the movement of molecules in a fluid or the diffusion of particles on a surface. The change in position is squared and then averaged for all tracked entities over a defined period. This process yields a value reflecting the extent of movement, offering insights into dynamic processes.

This analysis provides a fundamental metric for understanding diffusive behavior and characterizing the mobility of particles in various systems. Historically, it has been crucial in fields like physics, chemistry, and materials science for studying Brownian motion, diffusion coefficients, and the properties of materials. Its applications continue to broaden into areas such as biology and environmental science, enabling investigations into cellular transport, contaminant dispersion, and other complex phenomena. The insights gained are often crucial for modeling, prediction, and optimization.