C
OPYING PERMITTED PROVIDED
TI
COPYRIGHT NOTICE IS INCLUDED
34
G
ETTING
S
TARTED WITH
CBR
© 1997 T
EXAS
I
NSTRUMENTS
I
NCORPORATED
Teacher information
(cont.)
CBR plots—connecting the physical world and mathematics
The plots created from the data collected by
RANGER
are a visual representation of the
relationships between the physical and mathematical descriptions of motion. Students
should be encouraged to recognize, analyze, and discuss the shape of the plot in both
physical and mathematical terms. Additional dialog and discoveries are possible when
functions are entered in the Y= editor and displayed with the data plots.
0
A
Distance-Time plot
represents the approximate position of an object (distance from the
CBR
) at each instant in time when a sample is collected. y-axis units are meters or feet;
x-axis units are seconds.
0
A
Velocity-Time plot
represents the approximate speed of an object (relative to, and in the
direction of, the
CBR
) at each sample time. y-axis units are meters
à
second or feet
à
second;
x-axis units are seconds.
0
An
Acceleration-Time plot
represents the approximate rate of change in speed of an
object (relative to, and in the direction of, the
CBR
) at each sample time. y-axis units are
meters
à
second
2
or feet
à
second
2
; x-axis units are seconds.
0
The
first derivative
(instantaneous slope) at any point on the Distance-Time plot is the
speed at that instant.
0
The
first derivative
(instantaneous slope) at any point on the Velocity-Time plot is the
acceleration at that instant. This is also the second derivative at any point on the Distance-
Time plot.
0
A
definite integral
(area between the plot and the x-axis between any two points) on the
Velocity-Time plot equals the displacement (net distance traveled) by the object during
that time interval.
0
Speed
and
velocity
are often used interchangeably. They are different, though related,
properties. Speed is a
scalar
quantity; it has magnitude but no specified direction, as in “6
feet per second.” Velocity is a
vector
quantity; it has a specified direction as well as
magnitude, as in “6 feet per second due North.”
A typical
CBR
Velocity-Time plot actually represents speed, not velocity. Only the
magnitude (which can be positive, negative, or zero) is given. Direction is only implied. A
positive velocity value indicates movement away from the
CBR
; a negative value indicates
movement toward the
CBR
.
CBR
measures distance only along a line from the detector. Thus, if an object is moving at
an angle to the line, it only computes the component of velocity parallel to this line. For
example, an object moving perpendicular to the line from the
CBR
shows zero velocity.
