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Linear Motion Unit 1 Velocity and Acceleration Objectives: • Define the concept of average velocity in a way that shows you know how to calculate it • Calculate average velocity and to solve an equation involving velocity, distance, and time • Interpret and plot position-time graphs for positive and negative velocities • Determine the slope of a curve on a position-time graph/velocitytime graph and calculate the velocity or acceleration • Distinguish instantaneous from average velocity • Define average and instantaneous velocity • Be able to calculate average velocity, given two velocities and the time interval between them • Be able to calculate final velocity in the case of uniform acceleration • Be able to solve problems of motion of objects uniformly accelerated by gravity • Calculate distance fallen in an object affected by gravity • Learn to use an organized strategy for solving motion problems Speed • Instantaneous speed- – Example: Car speedometer • Average speed- Velocity Instantaneous velocityv = d t v = velocity, m/s d = displacement, m t = time, s d V t Average velocityCan you have a negative velocity? Why or why not? v = d t SI Units: m/s v = average velocity, m/s d = displacement, m t = time, s English: miles/hour Example 3.1 Suppose a 100 m walk takes 80 seconds. What is the average velocity? Example 3.2 In the Summer Olympics the 100-m race was won in 9.83s. Find the average velocity in m/s. Known Unknown Equation Example 3.3 (pg. 43) A. What is the average speed of a cheetah that sprints 100 meters in 4 seconds? B. How about if the cheetah sprints 50 meters in 2 seconds? Example 3.4 (pg. 43) If a car moves with an average speed of 60 km/h for an hour, it will have traveled a distance of 60 km. A. How far would it travel if it moved at a rate for 4 h? B. For 10 h? Example 3.5 (pg. 43) In addition to the speedometer on the dashboard of every car is an odometer which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one-half hour later, what has been your average speed? Example 3.6 (pg 43) Would it be possible to attend this average speed and never go faster than 80km/h? Position Draw a Graph of "Speeding Up" Time Graphing Velocity - Position Draw a Graph of "Slowing Down" Time Graphing Velocity - Position Draw a Graph of “Constant Speed” Time Graphing Velocity - Comparisons • http://www.exploratorium.edu/baseball/reactiontime.html reaction time activity • reaction time of fox sports science episode 3 – Any (approx. 12 minutes) • http://www.pbs.org/wgbh/nova/barrier/ - faster than sound information Acceleration Average accelerationa = v t a= v= t= SI units = m/s2 English: mi/h instantaneous accelerationa= v t v a t Example 3.7 Suppose you plan to attend the Pittsburgh Steelers home-opener. The distance from Hollidaysburg to Pittsburgh is 90 miles (145 km). a) If you are able to average 45 mph (20 m/s), how long will it take you to travel to the game? b) As you pull into the parking lot, you decrease your speed from 20 m/s to 0 m/s over a time period of 4.0 seconds. What is your acceleration? Example 3.8 A car accelerates along a straight road from rest to 28 m/s in 5.0 s. What is the magnitude of its average acceleration? Known Unknown Equation Example 3.9 (pg. 46) What is the acceleration of a race car that whizzes past you at a constant velocity of 400 km/h? Example 3.10 The velocity of a car increases from 2.0 m/s at 1.0s to 16 m/s at 4.5 s. What is the car’s average acceleration? Known Unknown Equation Example 3.11 A car goes faster and faster backwards down a long driveway. We define the forward velocity as positive, so backward velocity is negative. The car’s velocity changes from –2.0 m/s to –9.0 m/s in a 2.0s time interval. Find the acceleration. Known Unknown Equation What is going on in this graph? What can you tell from this graph? What can be read from this graph? Explain the motion shown in the graph Review!!!! Aristotle (384 - 322 BC) Earth-centric perspective Proposed Two Types of Motion: Natural Motion Objects in the universe have a proper place based on their nature. ROCK SMOKE FEATHER - . Heavier objects fall faster than light ones Violent Motion Resulted from pushing/pulling forces Sustained motion required a sustained force - Pushing and moving a heavy rock - Bow and arrow Copernicus (1543) Sun is the center of the solar system Galileo (1564-1642) Provided evidence that Aristotle's views were inaccurate. Leaning Tower of Pisa Experiment Inertia (Inclined Plane Experiments) Galileo's Labs Galileo's Inclined Plane Experiment Physics Unit 1 - Motion Name: ______________________ Period: _____ Data Table Angle of Incline (o) Distance Traveled (cm) Acceleration (m/s ) 2 - Acceleration due to gravity How Fast- Free Fall • Freefall- - occurs when gravity is the only force that acts on an object • - No air resistance (in a perfect world) Can take place when: • - an object is falling • - an object is rising • - an object is traveling at an angle • - an object is momentarily at rest at its highest point Freefall Continued Gravity(g)- force of attraction between 2 masses Terminal Velocity-constant maximum velocity reached by a body falling under gravity through a fluid g = 10 m/s g = v t 2 Example 3.12 (pg. 48-49) Using the speedometer on Figure 3.7 what would the speedometer reading be 5s after it drops from rest? How about 6s after it is dropped? 6.5 seconds? Example 3.13 The time the Demon drop ride at Cedar Point, Ohio is free falling is 1.5 s. What is the velocity at the end of this time? Known Unknown Equation Free Fall Lab Object Small blue square Medium blue square Large blue square Softball Acceleration(m/s2 ) How Far d = 0.5 gt2 Example 3.14 (pg. 50) A car steps off a ledge and drops to the ground in 0.5 seconds. A. What is it’s speed on striking the ground? B. What is its average speed during the 0.5 seconds? C. How high is the ledge from the ground? Additional Websites • • • • • • • • http://www.fearofphysics.com/Xva/xva.html http://www.fearofphysics.com/Fall/fall.html http://www.fearofphysics.com/Roller/roller.html http://video.msn.com/?mkt=en-us&brand=foxsports&vid=a8a602c9-7cb4409d-906a-3055adfc10af&from=Fox%20Sports&tab=g1196965174236 Jerry Rice and Chad Johnson – may not work, but google search http://video.msn.com/?mkt=en-us&brand=foxsports&vid=fce2cab5-a3004f78-880c-18be6d3e3fc2&from=Fox%20Sports&tab=g1196965174236 Ben Rothelsberger and getting off a pass- may not work, but google search http://www2.swgc.mun.ca/physics/physlets/motiona.html - position vs. time graphs http://www2.swgc.mun.ca/physics/physlets/motionb.html - velocity vs. time graphs http://www2.swgc.mun.ca/physics/physlets/motionc.html - acceleration graphs