021 Motion

Note that density was matter divided by space. In that formula space was cubed. Full three-dimensional space. In the world of physical science the degree is the number of dimensions.

This week we explore motion. Motion was first introduced in the day one lab. Space divided by time. In motion, space is not squared nor cubed. Space is to the first degree. Linear. One dimensional. Motion has a single direction.

Measuring motion requires measuring both space and time. Space is measured using meters or centimeters. Time is measured using seconds. Motion in a direction is called velocity in physical science. Motion without reference to a direction is called speed. Working with motion in a direction usually requires working with vectors and trigonometry. In this section we will restrict ourselves to straight line motion. In straight line motion velocity and speed are the same thing.

velocity = distance time

If the distance is measured between two points in space, and the time is measured between two points in time, then the above formula is sometimes expressed as "the change in distance" divided by the "the change in time." The Greek letter delta (Δ) is used for the words "the change in."

velocity = Δdistance Δtime = distance2distance1 time2time1

The above formula is mathematically the same structure as the formula for the slope of a line between two points.

slope = y2y1 x2x1

In physical science the relationship between distance, velocity, and time is often algebraically rearranged and written:

distance=velocity×time

A rolling marble passes 0 centimeters (cm) at a time of 1.5 seconds (s). The marble passes 100 centimeters at a time of 3.5 seconds. Calculate the velocity of the marble.

Alternate Monday introduction: A caster board can be ridden past eleven equidistant columns with "lap times" recorded for each column. The columns used were about 4.6 meters apart. As homework the students were to graph the time versus the distance and determine the slope of the line.

A graph of duration versus distance is a graph of time versus space. The linear relationship distance = velocity × duration is a relationship between time and space.

On a graph of duration versus distance one gets a straight line if the speed is constant. The actual path over the ground might be straight or curved.

Time versus space, space versus space graphs N S E W text layers Graph 1: Time vs space slope is velocity Space versus space Graph 2 time: duration (seconds) space: distance (cm) east-west space: distance (cm) space: dist (cm) north-south

In graph one on the left above, time is plotted against space in the form of duration in seconds against distance in centimeters. The object, for example a rolling ball, is moving at a constant speed. The graph on the right is a "bird's eye view" of a ball rolling in a parking lot. The ball may roll straight, left, or right. The speed of the ball along the path is not displayed by graph two. The curve seen is the curvature of the ball along the ground.

Note that in vector physics velocity is always a speed in a particular direction. Change the speed, and the velocity changes. Change the direction, and the velocity also is said to change. A ball moving at a constant speed on a curved path is changing directions. The speed is staying the same but the velocity is changing. This is the difference between speed and velocity. Speed has no specified direction, velocity has to take into account the direction.

Graphs of time versus space, duration versus distance, do not tell us the direction of motion. Time versus distance depicts only the speed as the slope of the line. If the slope is changing, then the speed is also changing.

Graph three shows a ball rolling with the speed of the ball changing.

SC 130 Lab Two background rectangle major grid lines axes x-axis and y-axis data points as circles text layers Graph 3: A rolling ball The ball is changing speed as it rolls time: duration (s) space: distance (cm) y-axis labels 0 114 228 342 456 570 684 798 912 1026 1140 x-axis labels 0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0

Note that the above graph says nothing about the direction that the ball is rolling. The information is only about how far a distance the ball has moved from zero centimeters in how long a duration of time in seconds.

Interactivity: How slow are you?

This activity is also an opportunity to introduce GPS receivers, their operation, the screens displayed, and differences among the GPS models in use in the class. This introduction is important to activity 071 later.

Using instruments that measure time and distance, determine your speed. Weather cooperating, as a class we will go outside and use global positioning satellite receivers to determine how slow we saunter, stroll, walk, stride, jog, or run.