Direct and Inverse Variation



1.  The amount of money C, paid for a car varies inversely to its age in years t.  If a 2 year-old car cost $20,000, how much will a 3 year old car cost?

a].  $30,000
b].  $10,000
c].  $13333.33


 

2.  When a car travels a fixed distance at a constant speed, the length of time traveled is inversely proportion to the rate r.  If a driver usually makes a trip in 5 hours at an average speed of 65mph, what would the travel time be if her rate of travel was reduced to 55 mph?

a].   k = 325
b].   5.9 hours
c].   3.25 hours



3. The circumference of a circle equals 3.14 times the diameter.   If the diameter is 12m, what is the circumference?

a].   37.68 m
b].   3.82 m
c].   15.14 m



4. Charles' Law tells us that the volume V of a gas at constant pressure is directly proportional to the temperature in degrees Kelvin (K). 

A constant-volume gas thermometer has a pressure (absolute) of 891 Pa at 297oK.   If the
pressure increases to 1343Pa (absolute), what is the new temperature in degrees K? Hint:   Find the value of k, then use Charles' Law.

Question courtesy of Dr. John Zelinsky.

a]. 3oK
b]. 448oK
c]. 99oK



5.  Boyle's Law states that pressure and volume for a gas are inversely related for a gas at a fixed temperature.

Air in a balloon has a volume of .175 m3 and exerts a pressure of 1.43*105 Pa(absolute).If the
volume changes to .194 m3, what is the new pressure (absolute) ?  Assume the temperature remains
constant. Hint:  Find the value of k, then use Boyle's Law.

Question courtesy of Dr. John Zelinsky.

a].  1.29*105 Pa
b]. 25025 Pa
c].  1.74*105 Pa

 


6. The period T of a pendulum is proportional to the square root of its length L.   If the period of a 4m pendulum 114s, what is the period of a 36m pendulum?

a].  k = 57


b].  342 s


c].   6 sec




Copyright © 2006 Donna Tupper.