Final answer:
The fan speed of a physics cart is the independent variable, acceleration is the dependent variable, and factors like the cart's mass could be constants. Understanding the relationship between force, mass, and acceleration is essential in problems involving uniformly accelerated motion.
Step-by-step explanation:
When manipulating the fan speed of a physics cart to make it run, the fan speed serves as the independent variable because it is the variable that you are changing intentionally to see the effect on the cart's acceleration. Because the cart's acceleration depends on the speed of the fan, the acceleration is considered the dependent variable. A constant in an experiment is a parameter that does not change during the course of the experiment, ensuring that any observed changes in the dependent variable are indeed due to the manipulation of the independent variable. One constant parameter might be the mass of the cart, which ensures that changes in acceleration are due solely to changes in fan speed and not to their mass. In studying motion at constant acceleration, it's crucial to understand that velocity changes at a constant rate, meaning that the object will continue to speed up as long as it is under a constant net force.
A conversation about accelerated motion generally involves concepts like force, mass, acceleration, and the relationship between them as per Newton's laws. As velocity and acceleration are both vector quantities, a change in velocity can occur even when there's a change in direction, resulting in acceleration due to the directional change of that velocity. This is a common situation in rotational motion where we use variables analogous to linear motion but adapted for motion along a curved path, such as angular velocity and angle of rotation.