Kinematics is the mathematical description of motion. We begin with motion along a straight line. Our primary tools will be an object’s position, velocity, and acceleration.

《 LOOKING BACK Sections 1.4, 1.5, and 1.6 Velocity, acceleration, and Tactics Box 1.3 about signs

Graphs are a very important visual representation of motion, and learning to “think graphically” is one of our goals. We’ll work with graphs showing how position, velocity, and acceleration change with time. These graphs are related to each other:

• Velocity is the slope of the position graph.

• Acceleration is the slope of the velocity graph.

Motion is change, and calculus is the mathematical tool for describing a quantity’s rate of change. We’ll find that

• Velocity is the time derivative of position.

• Acceleration is the time derivative of velocity.

A model is a simplified description of a situation that focuses on essential features while ignoring many details. Models allow us to make sense of complex situations by seeing them as variations on a common theme, all with the same underlying physics.

Free fall is motion under the influence of gravity only. Free fall is not literally “falling” because it also applies to objects thrown straight up and to projectiles. Surprisingly, all objects in free fall, regardless of their mass, have the same acceleration. Motion on a frictionless inclined plane is closely related to free-fall motion.

The equations of motion that you learn in this chapter will be used throughout the entire book. In Part I, we’ll see how an object’s motion is related to forces acting on the object. We’ll later apply these kinematic equations to the motion of waves and to the motion of charged particles in electric and magnetic fields.