Motion and Force

Chapter Twelve: Distance, Time, and Speed 12.1 Distance, Direction, and Position 12.2 Speed 12.3 Graphs of Motion

12.1 Direction Distance: the amount of space between two points. Giving Directions: include distance and direction. Navigation: Using compass directions to direct travel.

12.1 The position variable Motion is about knowing where things are and how they move. To understand where things are, we need to understand position.

12.1 The position variable Position is a variable and it is always relative to an origin, or the place where the object’s starting point was zero.

12.1 Forward and backward Position and distance are similar but not the same. Both use units of length. Distance can have only positive values.

12.1 Forward and backward Position uses positive and negative numbers. Positive numbers are for positions to the right (in front) of the origin. Negative numbers are for positions to the left (or behind) the origin.

12.1 Forward and backward Many variables can be positive or negative. These include position, speed, and force. These variables are called vectors because they can have a value and a direction. We use the term velocity to mean speed with direction.

12.1 Keeping track of where you are Pathfinder is a small robot sent to explore Mars. It landed on Mars in 1997. Where is Pathfinder now?

12.1 Keeping track of where you are Pathfinder keeps track of its velocity vector and uses a clock. Suppose Pathfinder moves forward at 0.2 m/s for 10 seconds. What is Pathfinder’s velocity?

12.1 Keeping track of where you are Suppose Pathfinder goes backward at 0.2 m/s for 4 seconds. What is Pathfinder’s velocity? What is Pathfinder’s change in position?

12.1 Keeping track of where you are The change in position is the velocity multiplied by the time.

12.1 Keeping track of where you are Each change in position is added up using positive and negative numbers. Pathfinder has a computer to do this.

12.1 Maps and coordinates If Pathfinder was crawling on a straight board, it would have only two choices for direction. Out on the surface of Mars, Pathfinder has more choices. The possible directions include north, east, south, and west, and anything in between.

12.1 Maps and coordinates Pathfinder’s exact position can be described with two numbers. These numbers are called coordinates. This graph shows Pathfinder at coordinates (4, 2) m.

12.1 Maps and coordinates The graph can also show any path Pathfinder takes, curved or straight. This kind of graph is called a map. Street maps often use letters and numbers for coordinates.

12.1 Vectors on a map Where are you compared to where you started? Suppose you run east for 10 seconds at a speed of 2 m/s. Then you turn and run south at the same speed for 10 more seconds. Where are you compared to where you started?