## Position, Displacement, and Average Velocity

3.1 Position, Displacement, and Average Velocity

### Learning Objectives

By the end of this section, you will be able to:

- Define position, displacement, and distance traveled.
- Calculate the total displacement given the position as a function of time.
- Determine the total distance traveled.
- Calculate the average velocity given the displacement and elapsed time.

### Position, Distance, and Displacement

To describe the motion of an object, you must first be able to describe its **position** (*x*): *where it is at any particular time*. More precisely, we need to specify its position relative to a convenient frame of reference.

Although position is the numerical value of *x* along a straight line where an object might be located, **displacement** gives the *change* in position along this line. Since displacement indicates direction, it is a vector and can be either positive or negative, depending on the choice of positive direction.

Displacement is the change in position of an object: .

We define **total displacement**, , as *the sum of the individual displacements*.

The magnitude of the total displacement should not be confused with the **distance traveled**. Distance traveled, *x*_{total} , is the total length of the path traveled between two positions.

### Average Velocity

The **average velocity** is a vector quantity that is simply the total displacement between two points divided by the time taken to travel between them. The time taken to travel between two points is called the **elapsed time** Δt.

**Practice!**

Practice 3.1.1 |
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To define the position of an object, you need to measure |

(a) The object’s distance from a reference point. |

(b) The object’s angle measured from a reference line. |

(c) The object’s speed from a reference point that is at rest |

(d) The object’s distance from a reference point and its angle measured from a reference line. |

Practice 3.1.2 |
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A car moves from position A to position B. Which vector best represents the car’s displacement? |

(a) |

(b) |

(c) |

(d) |

Practice 3.1.3 |
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One drop of oil falls straight down onto the road from the engine of a moving car every 5 s. The figure shows the pattern of the drops left behind on the pavement. What is the average speed of the car over this section of its motion? |

(a) 20 m/s |

(b) 24 m/s |

(c) 30 m/s |

(d) 100 m/s |

(e) 120 m/s |