3.1 Space and Position 1

Chapter Objectives Calculate time, distance, or speed when given two of the three values. Solve an equation for any of its variables. Use and interpret positive and negative values for velocity and position. Describe the relationship between three-dimensional and one-dimensional systems. Draw and interpret graphs of experimental data, including velocity versus position, and speed versus time. Use a graphical model to make predictions that can be tested by experiments. Derive an algebraic model from a graphical model and vice versa. Determine velocity from the slope of a position versus time graph. Determine distance from the area under a velocity versus time graph.

Chapter Vocabulary average speed constant speed coordinates coordinate system displacement instantaneous speed instantaneous velocity origin position rate slope time vector velocity

Inv 3.1 Position, Speed, and Velocity Investigation Key Question: How are position, speed, and velocity related? 4

3.1 Space and position In physics, the word position refers to the location of an object at one instant. A position is always specified relative to an origin. The net change in position relative to the origin is called displacement.

3.1 Position and distance Distance is related to, but different from, position. Distance is a measure of length without regard to direction.

3.1 Position in three dimensions Space is three dimensional, so position must also be a three- dimensional variable. Any position in space can be precisely specified with three numbers called coordinates.

3.1 Positive and negative Allowing x, y, and z to have positive and negative values allows coordinates to locate any position in all of space.

3.1 One dimensional problems In three-dimensional space, position is a vector. A vector is a variable that contains all three coordinate values. Motion in a straight line is easiest to analyze because it is one dimensional. However, even in one dimension there is an origin and positive and negative values are possible.

3.1 Speed and distance Speed is the rate at which distance changes. In physics, the word rate means the ratio of how much something changes divided by how long the change takes. Constant speed means the same change in distance is traveled every second.

3.1 Calculating speed The change in position is a distance traveled in a given amount of time. To calculate the speed of an object, you need to know two things: the distance traveled by the object the time it took to travel the distance

3.1 Calculating speed Since speed is a ratio of distance over time, the units for speed are a ratio of distance units over time units.

Calculating speed in meters per second A bird is observed to fly 50 meters in 7.5 seconds. Calculate the speed of the bird in m/sec. You are asked for speed in m/s. You are given distance = 50 m; time = 7.5 s Use v = d ÷ t Plug in values and solve. v = 50 m ÷ 7.5 s ≈ 6.67 m/s

3.1 The velocity vector The velocity of an object tells you both its speed and its direction of motion. A velocity can be positive or negative. The positive or negative sign for velocity is based on the calculation of a change in position. Two cars going opposite directions have the same speed, but their velocities are different— one is positive and the other is negative.

3.1 The velocity vector Velocity is the change in position divided by the change in time.