Time dilation, which can be derived from the Lorentz transformations is
t'=t/sqrt(1-v^2/c^2)
where t is the time interval in the rest frame, and t' is the interval in the lab frame.
This relationship is neither linear or exponential in v.
The relationship between fluid flow rate and flow radius is not linear nor exponential. It is described by the Hagen-Poiseuille equation which shows that the flow rate is directly proportional to the fourth power of the radius of the tube. This means that a small change in the radius of the tube can have a significant impact on the flow rate.
The most effective types of models to demonstrate the relationship between distance and time are typically linear models or exponential models. Linear models show a constant rate of change between distance and time, while exponential models are useful for demonstrating changing rates of distance covered over time. These models can help visualize how the distance traveled changes with time.
The relationship between fluid flow rate and flow tube radius is typically nonlinear and follows a power law relationship. As the flow tube radius increases, the flow rate also increases, but not in a linear fashion. Instead, the relationship is often modeled using equations involving powers or roots of the tube radius.
Linear speed is found by dividing the distance traveled by the time taken to travel that distance. It is the magnitude of the velocity vector and indicates how fast an object is moving in a straight line. The formula for linear speed is: Linear speed = distance ÷ time.
Linear speed is the distance traveled per unit of time along a straight path. It is a measure of how fast an object is moving in a specific direction. It is often calculated as the ratio of the distance traveled to the time taken to cover that distance.