Physci 02

Introduction to velocity

In chapter one density was matter divided by space. Space is measured in meters cubed or centimeters cubed. Space has cubic units exactly because space occupies three dimensions. In the world of physical science the degree of the exponent is the number of dimensions. Volumes occupy three-dimensions of space, extend in three directions.

Motion is space divided by time. For motion, space is not squared nor cubed. Space is to the first degree. Linear. One dimensional. Motion has a single direction, possibly as a line or a curve, but motion is one dimensional along that path. One cannot go three directions at the same time.

Measuring motion requires measuring both one-dimensional space, called distance, and time. Distance 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.

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."

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

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

distance = velocity × time

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.

Even if the path is curved, the distance covered along that curve is still the velocity × time. The time versus space graph says nothing about the shape of the path of the path.

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 on a time versus distance graph, then the speed is also changing.

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.

Rolling ball laboratory two

This laboratory explores the relationship between time and distance for an object moving at three different but constant velocities. As noted in the first laboratory, in physical science a "relationship" means how one variable changes with respect to another variable. This change is described using mathematical equations. Math is the language in which physics is "spoken."

Procedure

Roll a ball along a length of sidewalk that has distance measurements marked off. Or ride a RipStik over a premarked course. Or roll a marble across the floor with floor markings at regular intervals.  Time the passing of the marks with a chronograph that can record split times. Record the time in seconds versus the distance in meters. Make at least three sets of measurements (three tables) for a slow, medium, and fast motion. Is the relationship reasonably linear? How are velocity and slope related? What is the effect of a higher velocity on the slope? Are there indications that friction is affecting the results?