## SAT Physics Subject Test

## Chapter 2 Kinematics

**Kinematics** in many ways is the heart and soul of physics and, not surprisingly, a big deal on the SAT Physics Test. Kinematics is specifically the study of an object”s motion in terms of its **displacement** (position in space), **velocity** (how fast an object is changing position), and **acceleration**(how fast an object is changing its velocity). In this chapter, we will explicitly define these terms and investigate how they relate to one another. Additionally, we will go beyond one-dimensional motion and delve into two-dimensional motion, that is, the world of projectile motion.

### DISPLACEMENT

Displacement refers to an object”s **change in position**. It”s the vector that points from the object”s initial position to its final position, regardless of the path actually taken. Since displacement means change in position, it is symbolized as ∆**s**, where ∆ denotes change in and **s** means spatial location.

**Displacement: A Strange Trip**

The insect on the table below crawls 1 meter north, 2 meters east, 1 meter south, and finally 2 meters west.

Even though the insect has crawled a total distance of 6 meters, its displacement is 0 meters. During the course of the bug”s motion, it covered 6 meters of ground (distance = 6 m). Yet, when it is finished, it has not gone anywhere at all—there is no displacement for its motion (displacement = 0 m). Displacement is a vector quantity, and must incorporate **net** direction. The 1 meter north is canceled by the 1 meter south, and the 2 meters east is canceled by the 2 meters west.

If we know that the displacement is horizontal, then it can be called ∆*x*; if the displacement is vertical, then it”s ∆*y*. Displacement is a net change, so it may differ in magnitude from total distance traveled (though if the path is all in one direction, it will not). Since a distance is being measured, the SI unit for displacement is the meter: [∆*s*] = m.

1. A rock is thrown straight upward from the edge of a 30 m cliff, rising 10 m then falling all the way down to the base of the cliff. Find the rock”s displacement.

Here”s How to Crack It

Displacement refers only to the object”s initial position and final position, not the details of its journey. Since the rock started on the edge of the cliff and ended up on the ground 30 m below, its displacement is 30 m downward.

2. In a track-and-field event, an athlete runs exactly once around an oval track, a total distance of 500 m. Find the runner”s displacement for the race.

Here”s How to Crack It

If the runner returns to the same position from which she left, then her displacement is zero.

The *total* distance covered is 500 m, but the net distance—the displacement—is 0.

**Distance vs.Displacement**

Note that distance is

not the magnitude of the

displacement unless the

object has moved in a

straight line.