Velocity and Distance

1. Position and Distance Traveled on a Line
   For a point moving on a straight line, if its velocity at time is , and the position of the point at time is , the position of the point at time and the distance traveled by the point from time to are given by:
1. The position at time :
   
2. The distance traveled from time to :
   


2. Distance Traveled in a Plane
   For a point moving in a plane where its position at time is given by the functions and , the distance traveled by the point from time to is:
   

Arc Length of a Curve

1. Parametric Curve
   For a curve defined by , with no overlapping parts in the interval , the length of the curve is:
   
2. Function of Curve
   For a curve over the interval , the length of the curve is: