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## Linear Motion

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**Linear Motion**Or 1 Dimensional Kinematics**This problem was missed a lot of 1314 benchmark. Did not**put in signs for calculation • A car is traveling west and decreases its speed from 30 m/s to 23 m/s in 2 seconds. What is the car’s average acceleration? Include direction.**9/9**• Goal: Begin Motion • Pick up Sample WS & calculator. • Turn in Bubble Gum Lab to Sorter • If you were absent, pick up the Bubble Gum Lab from the mailbox. It will be due Thursday. • Tests are will be graded by tomorrow. • Solve Now in dim. Analysis format: • A starship travels at 6.5 x 108 m/sec. How far does it travel in one day?**9/10 If absent Tue, get Sample WS I**• Goal: Calculate practice: distance, displacement, speed and velocity • Tests are graded. Missing: Taylor Morgan,, RinaRraci, Katana Shoemake, Alexis Baldwin, Morgan Barrentine • Solve Now: • Thomas starts in a maze. He runs east for 10 m and hits a dead end. He then turns around and runs west for 15 m. What distance did he run? What is his displacement from his origin? Did he run into any Grievers?**9/11**• Have Linear Motion WS out to be checked • Pick up Acceleration WS and a calculator • Grades to date have been put in. There are quite a few zeros It is your responsibility to check gradebook. • This was what was turned in last week • Dim Analys WS (10 problems) due 9/2 • Tue 9/5 Sci Not practice due 9/2 • Safety Review due 9/4 • Sci Method Station due 9/5 • Bubble gum Lab due 9/8 • THIS WEEK ONLY, I will accept any of these assignments today since I was out of town last week.**Retests**Scored below 70 on original test Must come in and perform test corrections before or after school Retests only after school You must sign up at least one day in advance for a retake. You may not do a retake if you have not done test corrections.**How long does it take a motorcycle , initially at rest to**increase its speed to 15 m/s if it accelerates at 0.95m/s2? • How many centigrams in a gram? • How many meters in a kilometer?**Great Website for Linear Motion**http://www.glenbrook.k12.il.us/gbssci/phys/class/1DKin/U1L1a.html**Kinematics in one dimension**the study of linear motion (in a straight line -not curved)**Motion*** What does it mean for an object to be in motion? It is the change in position of an object as compared to a reference point**Is the brick wall moving?**Not from where she’s sitting, but…**…from space, the earth rotates and the wall with it.**So, whether or not something is moving depends on your frame of reference. ***Frame of Reference**a fixed point used to determine magnitude and direction of motion Magnitude? See Video Here**Rate**a change in a given quantity over a specified period of time (examples: velocity and acceleration) What are some units of measurement?**Scalar quantity**a measurement Magnitude No direction implied Ex. mass, volume, density, distance, speed**Vector quantity**a measurement Magnitude Direction Ex.: displacement, velocity, acceleration, force**Distance**the length of the actual path taken by the object regardless of direction scalar quantity SI units include m, km**Displacement**length (measured in a straight line) from the reference point to the object (implies a given direction) Sometimes on graph labeled as Position vector quantity SI units include m, km**Speed**change in distance divided by change in time s =d/t or v =d/t s is typically written “v” Where s = speed d = distance t = time scalar quantity SI units include m/sec or cm/sec.**Velocity**speed in a given direction magnitude and direction included in the measurement vector quantity SI units include m/sec or cm/sec. (v = ∆d/∆t) where ∆d= change in displacement (dfinal-dinitial) ∆t= change in time (tfinal-tinitial)**What is the unit for:**• Speed? • m/s • Velocity? • m/s • Acceleration? • m/s2**What is the displacement for Bob the Bear?**Dd = df – di Dd = 90m – 20m = 70m**Displacement is not always equal to distance travelled!**What is Clyde the Caterpillar’s displacement? Dd = df – di Dd = 80m – 20m = 60m**Sign for Vectors**the sign indicates direction can be positive or negative Right , East , or North are + Left, West, or South are -**What is the displacement for Frank the Fish?**-70m The negative sign tells us he is moving opposite the direction of the number line—in this case, to the left.**Ex 1**Travis needs his physics notes. He walks from his house 8 yards due east towards Shannon’s house to borrow her notes. At this point Travis realizes he left his phone at home and runs back to get it. After picking up his phone he continues the 14 yards east to Shannon’s house. What was the distance and displacement?**EX 1 Travis needs his physics notes. He walks from his**house 8 yards due east towards Shannon’s house to borrow her notes. At this point Travis realizes he left his phone at home and runs back to get it. After picking up his phone he continues the 14 yards east to Shannon’s house. What was the distance and displacement? Distance = 8yds + 8yds + 14 yds = 30 yds Displacement = +8yds + -8yds + +14 yds = +14 yds or 14 yds East**Average Velocity*** Change in position Change in time Dd Dt The average velocity of an object is defined as the displacement of an object divided by the time in which it took place. Average velocity = vavg = = d2-d1 t2-t1**Ex 2**A racing car driven by Speed E. Demon travels 480 kilometers in 2.0 hours. Calculate the average speed in km/hr and convert to m/s.**Ex 2 A racing car driven by Speed E. Demon travels 480**kilometers in 2.0 hours. Calculate the average speed in km/hr and convert to m/s. Step 1 List Variables d= 480 km v = ? t = 2 hrs Step 2 Show Formula (arranged to solve for unknown) v = d t Step 4 This problem requires dimensional analysis 240km 1000m 1hr = 33.33 m/s 2 hr 1 km 3600s Step 3 Show substitution (with units) and answer v = 480 km= 240 km/hr 2 hrs**Ex. 3**Sunday Driver takes her Cadillac for a spin and travels 50.0 km at an average speed of 35.0 m/s. How long (in seconds) was she driving her car? 1428.57 sec Remember to change km to m! t = d/v NOT dv**Sample 4**A car travels at a constant speed of 4m/s for 5s. How far does it go in m? d = vt 20 m**Skip this year**A car travels at 60 km/hr for 200 km. It then speeds up to 90km/hr and travels an additional 200 km. What is its average velocity?**Acceleration**change in velocity divided by change in time (a = ∆v/∆t) Where ∆v = (vfinal-vinitial) ∆t =(tfinal-tinitial) vector quantity SI units include m/sec2 or cm/sec2**Acceleration*** Change in velocity Change in time Dv Dt vf - vi tf - ti vf - vi t Mathematically, Avg acceleration = aavg = = =**Ex 1**A rocket takes off from rest from the launching pad. It accelerates to a speed of 150m/s during a time period of 10 seconds. What was the acceleration experienced by the rocket?**Ex 1 A rocket takes off from rest from the launching pad.**It accelerates to a speed of 150m/s during a time period of 10 seconds. What was the acceleration experienced by the rocket? Step 1 List Variables d= vi = 0m/s (at rest) vf = 150 m/s a= ? t = 10 sec Step 2 Show Formula (rearranged) a = vf – vi t Step 3 Show substitution (with units) and answer a = 150 m/s - 0m/s = 15 m/s2 10 sec**Ex 2**Suppose a treadmill has an average acceleration of 4.7 m/s2. If the treadmill starts at 1.7m/s, what would its velocity be after 150 seconds?**Ex 2 Suppose a treadmill has an average acceleration of 4.7**m/s2. If the treadmill starts at 1.7m/s, what would its velocity be after 150 seconds? Step 1 List Variables d= vi = 1.7 m/s vf = ? a= 4.7 m/s2 t = 150 sec Step 2 Show Formula (rearranged) vf = vi + at Step 3 Show substitution (with units) and answer vf = 1.7m/s + [(4.7 m/s2)(150 sec) vf = 706.7 m/s**9/12 Get a calculator and blue formula chart (by**calculators). Solve this now: Practice Problem A Quiz Today after warm up! What would the acceleration of a car be if it goes from 100.0 m/s to 80.0 m/s in 5s?**Practice Problem A**-4m/s2 What would the acceleration of a car be if it goes from 100.0 m/s to 80.0 m/s in 5s?**Acceleration WS 1**3. A runner takes off from rest at the starting line. He accelerates to a speed of 8.4 m/s during a time period of 3.2 seconds. What was the acceleration of the runner? 2.63 m/s2 4. A jet plane has an average acceleration of 23.8 m/s2. as it takes off from the ground. If it’s starting velocity as it leaves the ground is 29.4 m/s, what would its velocity be after 16 seconds? What would the final velocity be in km/hr? 410.2 m/s 1476.72 km/hr 5. Don’t worry about this one yet**5. A boat is sitting still. The driver starts the motor and**accelerates at a constant rate until he reaches a velocity of 12.5 m/s 87 meters later. How long does it take to achieve this speed? This is a 2 step problem.**Acceleration equations**• Remember velocity, displacement, and acceleration are all vector quantities. • Indicate direction • right or east: positive • left or west: negative**a – acceleration in m/s2**v - change in velocity in m/s vf – final velocity in m/s vi – initial velocity in m/s t or t – time interval in seconds d – displacement in m vavg = Δd/Δt a = Δv/Δt = vf – vi/t a = vf2 - vi2 2Δd Δd = viΔt + ½aΔt2 Δd = viΔt + .5aΔt2**Any of these formulas can be rearranged!!!**• How do we know which formulas to use? • DVVAT!!!!!**Example B**• A tricycle, initially traveling at 0.15 m/s, experiences an acceleration of 0.045 m/s2. • What is the velocity of such tricycle after a period of 15 seconds?**Example B**vi = 0.15 m/s a = 0.045 m/s2 t = 15 s vf = ? What equation? vf = vi + aΔt vf = 0.15 m/s +( 0.045 m/s2)(15 s) vf = 0.83 m/s