Rate is a quantity that describes how fast or slowly something happens. For
example, your reading rate is the number of words per minute that you can
read. You can measure reading rate by using a watch to measure the time
interval it takes to read a page from a book. Then count the number of words
on the page. Divide the number of words by the time interval, and convert
the result to a unit rate. (A unit rate is an equivalent ratio with a denominator
of one). As an example, suppose you read 450 words in 1.8 minutes. Your
reading rate is:
450 words
250 words
=
1.8 minutes
1 minute
or 250 words per minute
The data-transfer rate of a computer modem
is the number of bits of data per second that
the modem transmits or receives. If a
modem’s data-transfer rate is 50,000 bits per
second, how many bits can be transmitted in
10 seconds?
Your heart rate is the number of times per
minute that your heart beats. If you measure
15 beats in 15 seconds, what is your heart
rate?
Heart rate is number of
beats per unit time.
Rate is a ratio of a measured quantity to a time interval. The measured
quantities in the examples above are words, data bits, and heartbeats. Can
you name another rate? What is the measured quantity?
Rate =
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C HAPTER 3
RATE
measured quantity
time interval
In this chapter, you will study rates in the four energy systems. The
measured quantities and rates are different in each system.
In mechanical systems, the distance traveled by an object is a measured
quantity. This quantity is also called the change in the object’s position. You
can calculate your jogging rate by dividing the distance traveled, or your
change in position, by the time interval. This rate is your speed. Speed is a
measure of how fast an object’s position changes. If you speed up or slow
down your jogging rate, you can use the change in speed as a measured
quantity. In this case, acceleration is the rate calculated by dividing the
change in speed by the time interval. For an object moving in a straight line,
acceleration is a measure of how fast the object’s speed changes. Typical
units for speed are meters per second and miles per hour. Typical units for
acceleration are meters per second per second and miles per hour per minute.
Speed is distance traveled per unit time.
Acceleration is change in speed per unit time.
Fluid quantities can be measured using mass or volume. An IV fluid flows
from a bag, through a tube, and into a patient’s arm. The mass and volume
of IV fluid in the bag change. The mass flow
rate through the tube is the change in mass
divided by the time interval. The volume
flow rate is the change in volume divided by
the time interval. Typical units for mass flow
rate are grams per second and kilograms per
hour. Typical units for volume flow rate are
cubic centimeters per second, gallons per
minute, and liters per hour.
In electrical systems, the measured quantity is charge. In a wire or circuit,
the amount of charge flowing past a point divided by the time interval is
called the current. Thus, current is a measure of the amount of charge
flowing per unit time. Current is measured in units of coulombs per second.
One ampere is defined as one coulomb per second.
Thermal energy or heat is the measured quantity in thermal systems. Heat is
the thermal energy that flows from regions of higher temperature to regions
of lower temperature. Heat flow rate is a measure of how fast heat flows.
This rate is the ratio of the heat transferred to the time interval. Typical units
for heat flow rate are joules per second, calories per minute, and Btu per hour.
C HAPTER 3
RATE
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