4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

In straight-line motion, the position function s(t) gives the location of an object at time t. The first derivative, s'(t), is the velocity, which measures how position changes with time. The second derivative, s''(t), is the acceleration, which measures how velocity changes with time. These three quantities are directly connected: position tells where the object is, velocity tells how fast and in what direction it is moving, and acceleration tells how its motion is changing. This is one of the most important applications of derivatives in the course.