THE MATH OF PHYSICS
EQUATIONS• In physics, equations are used to show how different measured quantities are
related
• Each letter in this equation represents a different quantity or variable• d – distance (in meters, m)
• v - velocity (or speed) (in meters per sec, m/s)
• t – time (in seconds, s)
• v and t are written next to each other, so that means they are multiplied together
• d is all by itself on one side of the equal sign…… so this equation solves for d (distance)
• written as a sentence ….“Distance is equal to speed multiplied by time”
d = v t
UNITS• Units (or labels) need to be included with all quantities
• How tall are you?
• 60
• ????
• Quantities make no sense without UNITS!!!
UNITS BEHAVE LIKE NUMBERS!
• Units behave like numbers
• When a number is divided by itself, the number cancels out leaving a 1.
•
• Any whole number can be written as a fraction with a 1 as the denominator
•
SEE HOW NUMBERS CANCEL…..
DIAGONALS CANCEL
UNITS WORK THE SAME WAY….
ANOTHER EXAMPLE
FOR ANY EQUATION… • The Units must be the same on both sides of the equal sign
Units on both sides of the equal sign are equal to ‘m’!!
MOTION FORMULA ---
3 Motion Formulas
Solve for Distance d = vtSolve for Speed (or velocity) v=d/tSolve for time t = d/v
d = v t
Do units agree on both sides of each of these equations???
EXAMPLE PROBLEM
• A car travels at 5 m/s for 120 s. How far has the car travelled?
• What are they asking for?
• What do you have?
• What equation is best?
• Plug in and Solve!
EXAMPLE PROBLEM 2
• A runner travelled 400 m in 80 s, how fast was the runner??
• What are they asking for?• What do you have?• What equation is best?
UNIT CONVERSIONS
• Conversion factors are used to cancel out unwanted units and acquire desired units
• 1 yard = 3 feet
• 150 ft = _______ yds
• 1kg = 2.2 lbs
• 50 kg = _____ lbs
• 5280ft = 1 mi
• 3000 ft = ________ mi
MORE UNIT CONVERSIONS
• 1 N = .22 lbs
• 7 lbs. = ________
• 1 km = 0.6 mi
• 10 km = _____________ mi
STANDARD (FUNDAMENTAL) UNITS (SI) --- METRIC UNITSQuantity UnitLength (distance) Meters (m)Time Seconds (s)Mass Kilograms (kg)Temperature Kelvin (K)Velocity Meters per second (m/s)Acceleration Meters per second per second (m/s2)
METRIC PREFIX CONVERSIONS
• Important ones• Milli• Centi• ….. Base• Kilo
PRACTICE QUESTIONS ABOUT METRIC UNITS• How many meters in a Kilometer?
• How many centimeters in a meter?
• How many millimeters in a meter?
• How many grams in a kilogram?
• 340 g = _________________ kg
• 230 cm = _______________ m
• 3.5 km = ________________ m
• 4500 m = ________________ km
VISUALIZING UNITS
• Activity in library after in class demo’s.