Linear Motion Begins with a Frame of Reference!

Frame of Reference Distance, Directions and Displacement are always measured relative to a frame of reference

SI Units (International System of Units) Length-Meter Mass-Kilogram Time-Second Electrical Current -Ampere Temperature-Kelvin Amount of -Mole Substance

Frame of Reference The Earth is rotation once every 24 hours Circumference of earth is 24,000 miles at the equator At the equator a person is traveling at approximately 1000 mph The circumference of earths orbit is 940 million Kilometers The earth is rotating around the sun at 107,306 km/hr The earth rotates around the milky way galaxy at 900,000 km/hr

Distance vs. Displacement Distance Displacement

Distance vs. Displacement Distance -A scalar quantity which refers to how much ground an object has covered Displacement -A vector which refers to the object’s overall change in position Scalars are quantities which are fully described by a magnitude (or numerical value) alone. Vectors are quantities which are fully described by both a magnitude and a direction.

Activity

Measuring Displacement What is the displacement and distance traveled? Distance = 420 m Displacement = 140 m right

Measuring Displacement Mr. Hamann is recruited for his ninja like skills as a Formula 1 racecar driver. After winning the Indy 500 he contemplates what his Distance and Displacement were. Distance = 500 Miles Displacement = 0 miles

Speed Speed is the ratio of the distance an object moves to the amount of time the object moves. Or….how fast an object moves Average Speed - Over the entire trip Instantaneous Speed -At a moment in time

Speed Avg. Speed = Total Distance/Total Time Avg. Speed = ∆ d/ ∆ t ∆ = change in ∆ d = d 2 -d 1 ∆ d = 4.0km- 0 Exp: A person jogs 4.0 km in 32 minutes what is his avg. speed in m/s? Avg. Speed = (4.0 km * 1000m/km) / (32 min * 60 s/min) = 4000 m/1920 s = 2.1 m/s

Distance / Time Graphs Constant speed vs. Varying speed

Distance / Time Graphs Avg. Speed = ∆ d/ ∆ t Avg. Speed = Slope Distance Time

Instantaneous Velocity Time Distance v = 20 m/s v = -15 m/s v = 4 m/s

e-time-graph-activity.phphttp://graphs.mathwarehouse.com/distanc e-time-graph-activity.php

Rolling Marble of Doom! 1.Form a ramp by placing 1 end of the ramp on a stack of 6 identical books. 2.Release the marble at the top of the ramp and use a stopwatch to measure the time it takes for the marble to reach the bottom 3.Record this time 4.Prediction: How many books tall would the stack have to be to double the time required for the marble to reach the bottom of the ramp? 5.Record this prediction 6.Test your prediction. Remove one book at a time and repeat step 2 until there is only 1 book left. 7.Make a table and graph the resulting speed. 8.How much time does the marble need to get to the bottom of a horizontal ramp? 9.If an infinite number of books were added to the stack would the time required for the marble to reach the bottom continue to decrease? Explain.

Velocity Why do cars have a speedometers and not velocimeters? Velocity describes both speed and direction Velocity is a vector! Mr. Hamann’s Ninja car is traveling around the track at 120 km/hr What is the velocity at this point? Is the velocity constant?

Velocity Constant Velocity Constant speed and constant direction Combining Velocities Lesson in Vector Addition 5 m/s 10 m/s

Combining Velocities 5 m/s 10 m/s Boat was traveling at 10m/s with the current on a river moving at 5m/s Boat was traveling at 10m/s against the current on a river moving at 5m/s Relative to the river bank 10 m/s+ 5 m/s = 15 m/s 10 m/s 5 m/s 10 m/s – 5m/s = 5 m/s

Combining Velocities Ninja boat is traveling across a river at 10 m/s while the current pushes it sideways at 3.0 m/s 3.0 m/s 10.0 m/s 3.0 m/s a 2 + b 2 = c 2 c 2 = √ a 2 + b 2 = √ (10 m/s) 2 + (3m/s) 2 = √ (100m 2 /s 2 + 9m 2 /s 2 ) = √ 109 m 2 /s 2 = 10.4 m/s

Vector Direction 3.0 m/s 10.0 m/s θ 10.4 m/s

Vector Direction SOH CAH TOA Sin θ = 3.0 / 10.4 Sin θ = 0.29 Θ = 17° 3.0 m/s 10.0 m/s θ 10.4 m/s

Labs Physics 500 Frisbee velocity Velocity of sinking marble Probeware cart on ramp Cannon Balls launch velocity Domino Effect

Acceleration Acceleration – the rate at which velocity changes So it is technically a rate of a rate A change is speed, change in direction, or changes in both Acceleration is a vector Acceleration avg = Change of velocity/ Change in Time = ∆v / ∆ t = (v f – v i ) / (t f - t i )

Acceleration Acceleration – the rate at which velocity changes So it is technically a rate of a rate A change is speed, change in direction, or changes in both Acceleration is a vector Acceleration = Object speeds up?

Acceleration We feel acceleration all the time –Cars Gas pedal Brakes Steering wheel –Planes –Gravity

Vomit Comet

Question? Suppose a velociraptor moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 50 km/h, then from 50 to 70 km/h. What is this dinosaur’s acceleration in each of these time intervals?

Answer Acceleration= (40km/h-35km/h) / 1 s = 5 km/h /1s = 5 km/h *s = 1.39 m/s 2 Acceleration= (50km/h-40km/h) / 1 s = 10 km/h /1s = 10 km/h *s = 2.78 m/s 2 Acceleration= (70km/h-50km/h) / 1 s = 20 km/h /1s = 20 km/h *s = 5.55 m/s 2 Acceleration = Change of velocity/Time = ∆v / ∆ t = (v f – v i ) / (t f – t i )

Measuring Acceleration Lab Personal Acceleration and Top Speed Objective: Determine your top speed and rate of acceleration from a motion graph Equipment: Pasco DataStudio© motion detector or other timing device Methods and Analysis 1. Line yourself up with the motion detector near the back of the room. Your partner will hit the Start button and cue you to start running to top speed as fast as you can. Be sure to run the designated line so that you remain in line with the motion detector. 2. Print your graph from the computer. This will be a distance-time graph. Indicate on your graph where you are accelerating and where your velocity is constant. 3. Determine where your velocity is constant on the graph, draw a line to best fit this region, then find the slope. Record this as your top speed in both m/s and km/hr. 4. Based on the time and distance to reach your top speed, calculate your rate of acceleration in m/s2. Compare this value to the acceleration of gravity (9.8 m/s2). 5. Compare your top speed with the fastest ever recorded human speed of Donovan Bailey, m/s. 6. If Donovan Bailey reaches top speed in 3.00 seconds, what is his rate of acceleration? 7. On your graph, sketch a runner with a rate of acceleration higher than yours and label as a higher. 8. Accurately sketch a velocity vs time graph of your motion out to 10 seconds. 9. Summary.

Free -Fall Time(s)Instantaneous velocity 00 m/s 110 m/s 220 m/s 330 m/s 440 m/s 550 m/s ……. t10*t m/s When Dealing with free fall 10m/s 2 is the acceleration do to gravity

Free -Fall v= gt (How fast) Where g= acceleration due to gravity on earth »g= 9.8m/s 2 If Acceleration due to gravity is constant on earth why are we hesitant to catch a baseball dropped off the empire state building?

Speed vs time graph 1s 0s 3s 2s 5s 4s 7s 6s v= 20m/s v= 30m/s v= 0 m/s v= 10m/s v= 30m/s Time speed Slope = acceleration v= 40m/s v= 20m/s v= 10m/s

Lab - Free fall exploration-find acceleration (physical science easyplanner p.234 TAP : Measuring the acceleration of free fall

Acceleration v= at (How fast)

Rocket Sled What is the acceleration of a rocket sled that goes from 0 to 700mph in 2.1 seconds? v = at 313 m/s = a(2.1) a = 149 m/s 2 How far does this Rocket sled travel in 2.1 seconds when starting at rest? D = ½ at 2 D = ½ (149) 4.4 D = 2.2(149) D = 328 m

Motion at constant Acceleration Why does v=at? Avg. Velocity = ∆ d/ ∆ t (direction) v avg = (x f – x i ) / (t f - t i ) –Since t i =0 then… v avg = (x f – x i ) / t a = (v f - v i ) / t v = v i + at

Free –Fall How Far? Time(s)Distance Fallen (m) ……. t½ gt 2 When Dealing with free fall 10m/s 2 is the acceleration do to gravity

Free -Fall How Far? d = ½ at 2 Time (s) Speed (m/s) Distance (m) Time (s)

Time (s) Distance (m) Time (s) Time (s) Acceleration m/s Speed (m/s)

Reaction Time How fast is your reaction time?

Reaction Time d = ½ at 2 t= √(2d/g)