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.