position function (2.1)
function that shows the location of an object at a given time; ex. h(t) = 100 – 16t^2
In calculus, the term position function generally refers to a function that describes the position of a moving object at a given time. More specifically, the position function indicates the object’s location with respect to a fixed point, typically the origin of a coordinate system.
The position function, denoted by s(t), is a mathematical representation of the distance travelled by the object up to time t. In other words, if an object is moving in a straight line and its position at time t is given by s(t), then the distance travelled by the object from the starting point up to time t is s(t).
The position function can be either a continuous or a discontinuous function depending on the nature of the motion of the object. For example, if an object is moving at a constant rate, then its position function will be a linear function of time. However, if the object is accelerating or decelerating, then its position function will be a nonlinear function of time.
It is worth noting that the position function is a fundamental concept in calculus and is used extensively in the study of motion, optimization, integration, and differentiation.
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