I can . . . explain the difference between average speed and instantaneous speed. explain the difference between speed and velocity. explain the difference between velocity and acceleration. explain the meaning of the slope of a graph involving position, velocity, or acceleration with respect to time. recognize the appropriate units of each concept.

Rate is defined as: Examples: Any Quantity divided by Time Inches of Rain per Hour Pizzas per Day Vibrations per Second

relative to something else. Speed is the RATE at which your position changes relative to something else.

Moving relative to what? LINEAR MOTION Is this car “moving”? Moving relative to what? http://galenfry.com/nz/devon11.jpg

Relative Motion 15 knot wind 15 knot sailboat What is the speed of the wind relative to the boat? http://commons.wikimedia.org/wiki/File:Clouds_over_the_Atlantic_Ocean.jpg http://1.bp.blogspot.com/-p304Z4BxlOI/T6l6H5l231I/AAAAAAAANK0/ZsIm2jbM_s8/s1600/20120413%2BTexoma%2B3454%2B74%2Bspinnaker%2Bout%2BJ122%2BSecond%2BStar.jpg

Change in Position Time Average Speed ≡ ∆ x t ≡ http://www.clarkstopwatch.qpg.com/ ÷

Distance Time Average Speed = http://www.clarkstopwatch.qpg.com/ ÷

Units miles hour meters second inches minute centimeters year

Fundamental Units M.K.S. System Meters Kilograms Seconds

All Possible Units American Metric (SI) M.K.S Feet Yards Inches Miles Ounces Gallons Pounds Cups Teaspoons Centimeter Millimeter Liter Milliliter Grams Hours Minutes Days Years Seconds M.K.S Meters Kilograms Thingamajigs Two shakes of a lambs tail Jiffy Bushel

328 ft 19.678 s = 16.7 ft s 1 mi 5280 ft 3600 s 1 hr 11.4 mi hr

Average Speed ≡ ∆ Position ∆ Time Rise Run = ∆ Y ∆ X Slope ≡

Average Speed ≡ Slope ≡ Rise Run = ∆ Y ∆ X ∆ Position ∆ Time

Circumference = 2·π·6,378 km = 40,070 km 40º 6,378 km Circumference = 2·π·6,378 km = 40,070 km Speed = 40,070 km 24 hr = 1670 km/hr

Circumference = 2·π·149,500,000 = 939,336,203 km 939,336,203 km 365 days 939,336,203 365 · 24 1 day 24 hr = = 107,000 km/hr

246,000,000,000,000 km 223,000 years 6,930,000,000 km/hr 220 km/sec

If a car has an average speed of 48 If a car has an average speed of 48.3 meters per second, how long will it take to travel a distance of 6,740 m? V = d t

If a car has an average speed of 48 If a car has an average speed of 48.3 meters per second, how long will it take to travel a distance of 6,740 m? V = d t Write down the EQUATION! 48.3 = 6740 t t Plug numbers into the EQUATION! t 48.3 48.3 Carefully use ALGEBRA to solve the equation. t = 6740 48.3 t = 1.40 x 102

Your speed at any given moment Instantaneous Speed Your speed at any given moment

Average speed from 3 to 8 seconds Average speed from 3 to 6 seconds 270 meters Average speed from 3 to 4 seconds Instantaneous speed at 3 seconds

Is driving 1100 miles in 13 hours reasonable? Distance Time Average Speed = 1100 miles 13 hours = 85 mi hr =

NO! 85 mph AVERAGE 50 + 100 + 0 + 67 + 125 + 67 6 68 mph 125 mph 50 + 100 + 0 + 67 + 125 + 67 6 68 mph

“B” Which ball gets to the finish line first? It has a higher average speed!

Velocity ≡ Speed in a Given DIRECTION Speed vs. Velocity Velocity ≡ Speed in a Given DIRECTION SPEED: 55 miles hour VELOCITY: 55 East miles hour

180 mph 180 mph

180 mph Same SPEED 180 mph Different VELOCITIES

Change in Velocity Time ≡ Acceleration ∆ V t ≡ ÷ 50 miles hour 70 10 sec http://www.clarkstopwatch.qpg.com/

Acceleration ≡ = = = 2 = 2 ∆ Velocity Time Vf – V0 t 70 – 50 10 sec mi hr = 2 mi hr sec mi hr 1 sec 1 = 2 mi hr ·sec

Acceleration = 10 mi/hr/s Acceleration = 5 mi/hr/s ? ? Acceleration = 10 mi/hr/s Acceleration = 5 mi/hr/s 10 20 30 40 50 60 70 80 90 100 110 120 130 10 20 30 40 50 60 70 80 90 100 110 120 130 miles per hour miles per hour 3 4 5 1 2 10 9 8 7 6 6 3 2 1 9 4 10 5 8 7 Time = s

Name THREE controls on car that cause the car to ACCELERATE. Acceleration Δvelocity Time ≡ Name THREE controls on car that cause the car to ACCELERATE. Gas (accelerator) Brake Steering Wheel

Acceleration is a CHANGE in VELOCITY over time. You can change your velocity by EITHER changing your SPEED or your DIRECTION. 70 mph 70 mph

Acceleration ≡ ∆ Velocity ∆ Time Rise Run Average Acceleration Acceleration ≡ ∆ Velocity ∆ Time Rise Run = ∆ Y ∆ X Slope ≡

Acceleration

Field Trip! 5 ft 4 ft 3 ft 2 ft 1 ft

Change in Velocity Time ≡ Acceleration ∆ v t a = m s s a = 5 Example: m s 1 s 1 m s·s a = 5 m s2 a = 5

What is the instantaneous velocity after 30 seconds? m s2 Acceleration = 5 EVERY second the velocity changes by 5 m/s What is the instantaneous velocity after 30 seconds? 35 7 30 6 25 5 20 4 15 3 10 2 1 Instantaneous Velocity (m/s) Time (seconds) Vf = a·t Vf = 5·0 = 0 Vf = 5·1 = 5 Vf = 5·2 = 10 Vf = 5·3 = 15 Vf = 5·4 = 20 Vf = 5·5 = 25 Vf = 5·6 = 30 Vf = 5·7 = 35 Vf = 5·30 = 150

vx = +100 m/s + (5 m/s2)(30 s) = 250 m/s vx = +100 m/s + (- 5 m/s2)(30 s) = -50 m/s vx = -100 m/s + (- 5 m/s2)(30 s) = -250 m/s

I can . . . explain the difference between average speed and instantaneous speed. explain the difference between speed and velocity. explain the difference between velocity and acceleration. explain the meaning of the slope of a graph involving position, velocity, or acceleration with respect to time. recognize the appropriate units of each concept.