MOTION - I
PRELAB
PURPOSE
To study the concepts of distance
and velocity through graphical analysis
EQUIPMENT
human subjects, motion detector w/interface, masking tape
RELEVANT EQUATIONS
v = ( x - xo ) / t
v = vo + a t [for constant a]
x = vo t + ½ a t2 [for constant a]
DISCUSSION
The concepts associated with motion are central to all of physics. It is important to understand exactly what is meant by position, time, time interval, average velocity, instantaneous velocity, and acceleration. The concept of velocity as the time rate of change in the distance covered is fundamental. In graphical terms, the velocity of a body can be calculated from a plot of position vs. time. In order to do this, the graphical concept of the slope must be understood. Consider the plots illustrated in Figure 2-1:
Figure 2-1: Plots of Position vs. Time
In plot (a), the x-position of the body does not change with time. If you think about it, the velocity of such a body is zero. This is illustrated by the slope of the line that represents x vs. t. The slope is defined as the "rise" (Δx) over the "run" (Δt), and since we have zero rise everywhere on the plot, the velocity is zero everywhere.
In plot (b), the body is definitely moving, and the curve that represents x vs. t is a straight line. Calculating the slope is indicated for a particular spot on the curve where the rise and the run have been drawn. You will notice that the slope would be the same no matter where along the line we choose to calculate it. The velocity is therefore constant for this plot. Actually it was also constant, with a value of zero, for plot (a). Any time the x vs. t plot is a straight line (linear), the velocity is constant during that interval.
Next, in plot (c), we see that the variation of x vs. t is curved. This presents a problem if we want to find the slope---where's the straight line? The answer is to draw the tangent line at a given point on the curve. This is a unique straight line that touches the curve at one and only one point. The slope of the tangent line is the velocity at that point. In this context, the velocity is referred to as instantaneous, because it changes from instant to instant. You can qualitatively verify this fact by sketching in tangent lines near t = 0 and near the maximum value of t that is plotted. The slope of the tangent line, and therefore the velocity, starts out small but continues to increase as time elapses. This motion is one where the body is continuously speeding up, or accelerating.
Bear in mind that as a vector quantity, velocity also has direction associated with it. In motion along a straight line path, we distinguish the two possible directions with a plus or minus sign.
In this experiment you will explore these concepts in a direct, graphical way. You will use a motion detector interfaced to a computer to collect and display data. The following features are important for this experiment:
Print out and complete the
Prelab questions.