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Speed, Velocity and Acceleration Linear Motion Linear Motion • The following quantities are used to describe motion: speed, velocity and acceleration • Each of these is a rate. A rate is a quantity divided by time. • Motion along a straight line is sometimes called linear motion. All Motion is relative • All motion is relative to a reference. • In our environment, the reference for motion is the earth’s surface, and speeds are measured relative to the earth • The earth moves at 107,000 km/h relative to the sun Speed • Speed is a measure of how fast something is moving. • Units of speed could be: km/h, m/s, mi/h, ft/s • In physics we use units of m/s for speed • s = d/t distance speed d time s t Instantaneous Speed • Instantaneous speed is speed at any instant in time. • A speedometer measures speed in ‘real time’ (the instantaneous speed). Average Speed • Average speed is the average of all instantaneous speeds; found simply by a total distance/total time ratio • The average speed of a trip: total distance average speed elapsed time Velocity vs. Speed • Speed refers to how quickly an object moves • Velocity is defined as speed in a given direction or rate of change of position (displacement over time). v = x/t • Velocity refers to both the speed and direction • Negative velocity means the object is moving in the opposite direction • Motion at constant velocity means that both the speed and direction of an object do not change. • In a car, we can change the velocity three ways: gas pedal to speed up, brake to slow down or steering wheel to change direction Velocity Triangle • Speed and velocity triangles are similar because v = x/t • Find the equation for displacement, and time using the triangle • x=vxt • t = x/v x v t Velocity Questions 1) How far does Bob run if he maintains an average velocity of 3 m/s for 10 s? 2) List three ways you can change the velocity of your car. 3) Is it possible to go around a corner without changing velocity? Explain. 4) One car is going 25 miles/hr north, another car is going 25 miles/hr south. Do they have the same velocity? Explain. 1. What is the speed of a truck that travels 10. km in 10. minutes? 2. What distance is traveled by a police car that moves at a constant speed of 1.5 km/minute for 5.0 minutes? 3. What distance would be covered in 10. minutes by a train that travels at a constant speed of 500. meters every 10. seconds? 4. What is the average speed of a commercial jet that travels from New York to Los Angeles (4800 km) in 6.00 hours? 6. A car is traveling at an average speed of 70. m/s. How many km would the car travel in 6.5 hours? The pilot of a light plane heads due North at an airspeed of 180 km/h. A wind is blowing from the West at 60. km/h. What is the plane’s velocity with respect to the ground? A car moved 60 meters West in 2 hours. What is its average velocity? A moon rock is for the rock to fall 6.6 meters dropped from a cliff and it takes 2 seconds. What is the moon rock’s average speed? A car travels 1000 meters in 5 seconds. What its average velocity? A boy walks 500 meters in 10 seconds. What is his average velocity? Jane rolled a ball 600 meters. What was her average velocity if it took her 10 seconds? What is the average velocity of a dog that runs 7500 meters that in 10 seconds? What is the average velocity of a car that coasts 3000 meters in 300 seconds? How far will a horse trot at a velocity of 4 m/s for 1 minute? What is the average velocity of a student who walks 800 meters in 78 seconds? What is average velocity of a dog who walks 100 meters in 20 seconds? An object travels at a velocity of 18.99 m/s for a time period of 15.63 seconds. What is its displacement? An object travels at a velocity for a time period of 12.19 seconds over a displacement of 10.56 meters. What is the value of this constant velocity? An object travels at a constant velocity of 14.23 m/s for a time period of 11.19 seconds. What is its displacement over this time? An object travels at an average velocity of 15 m/s for 23 seconds. What is its displacement over this time? How long will a dog run at a pace of 2 m/s over 12 meters? Acceleration • For its velocity to change, an object must accelerate. • An object accelerates whenever its speed or direction or both change. • Acceleration may be positive (increasing speed) or negative (decreasing speed). • Acceleration is a measure of how quickly the velocity changes: a = Dv/t change of velocity acceleration time interval Acceleration at constant speed • An object moving in a circle at constant speed is always accelerating (changing direction). Solving Acceleration Problems using Acceleration Triangle • If not, use triangle to find change in velocity (Dv), then find initial or final velocity • Dv = ending velocity – starting velocity • Acceleration = Velocity Final – Velocity Initial » Time Dv a t A dragster going at 15 m/s increases its velocity to 25 m/s in 4 seconds. What is its acceleration? The driver of a car steps on the brakes, and the velocity drops from 20 m/s to 10 m/s in a time of 2 seconds. Find his acceleration. Find the acceleration of a car that travels at a constant velocity of 45 Km/hr for 10 s. Challenge: Calculate the velocity of a skateboarder who accelerates from rest for 3 seconds down a ramp at an acceleration of 5 m/s2. A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration? . A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration ? Is this acceleration higher than that of a car which accelerates from 0 to 30 m/s in 8 seconds? A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. Find the car’s average acceleration. 4. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard’s average acceleration? 5. If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s/s for 3 seconds, what will its final velocity be? A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration? A car accelerates at a rate of 3.0 m/s2. If its original speed is 8.0 m/s, how many seconds will it take the car to reach a final speed of 25.0 m/s? While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.) A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a period of 4.5 seconds. What is the acceleration of the dragster? A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at -4.0 m/s2? If a car can go from 0 to 60 mi/hr in 8.0 seconds, what would be its final speed after 5.0 seconds if its starting speed were 50 mi/hr? A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s2. If the cart has a beginning speed of 2.0 m/s, what is its final speed? A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of this helicopter? As she climbs a hill, a cyclist slows down from 25 mi/hr to 6 mi/hr in 10 seconds. What is her deceleration? A motorcycle traveling at 25 m/s accelerates at a rate of 7.0 m/s2 for 6.0 seconds. What is the final speed of the motorcycle? A car starting from rest accelerates at a rate of 8.0 m/s/s. What is its final speed at the end of 4.0 seconds? After traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the runner’s acceleration? Free fall, an example of acceleration • Free fall is when an object is falling being affected only by gravity. That means NO air resistance. Free Fall – All objects fall at the same rate • If you drop a coin and a feather at the same time you will notice that the coin reaches the ground way before the feather. • However, if you were to take the air out of the container you would find that the coin and feather fall together and hit the bottom at the same time! Acceleration due to gravity, g • Newton told us that every object with mass attracts every other object with mass and the size of the attraction depends on the mass of each object and the distance between the objects • We don’t feel the attraction of most objects because their mass is small relative to the Earth which has a huge mass. • The Earth pulls so that objects experience an acceleration of about 9.8 m/s2. This acceleration is given a special letter, g. • g = 9.8 m/s2 This number is important, remember it! • So during each second an object is in free fall, its velocity increases by 10 m/s. If the object experiences air resistance its velocity won’t increase as fast because air resistance will slow it down. Challenge Question • Suppose someone throws a ball straight upward with a speed of 30 m/s and at the same time throws one straight down with a speed of 30 m/s. Which ball will be traveling faster when it hits the ground, the one thrown straight upward or the one thrown straight down? Assume there is no air resistance. Time and velocity for an object in free fall v = gt v g t Time and Distance for an object in free fall d = ½ gt2 2d t g Free Fall Questions – How Fast? 1) When a ball is thrown straight down, by how much does speed increase each second on Earth? 2) When a ball is thrown straight up, by how much does speed decrease each second? 3) In free fall, do a feather and a ball fall side by side? Explain. 4) An apple falls freely from rest for 8 s on Earth, find its speed at 8 s. 5) Suppose a rock is dropped on a planet where the acceleration due to gravity it 5 m/s2, by how much would the speed change each second? 6) If a rocket on the planet in #5 falls from rest for 3 s, what is its speed at the end of the 3 s interval? 7) Challenge: Find g on a planet where a rock has a velocity of 120 m/s after 6s of free fall. Free Fall Questions – How Far? 1) For a freely falling rock does the distance fallen each second stay the same, increase with time, or decrease with time? 2) A ball is dropped from rest and freely falls for 6 s. How many meters has it fallen in 6 s? 3) A ball is thrown straight upward and travels 5 m until it reaches the top of its path. a) How far will it fall before it reaches its initial position? b) How long will it take to fall that distance? c) How long will the ball be in the air? 4) A ball is thrown straight up and returns to Earth 6 s later. a) Find its speed at the top of its path. b) Find its acceleration at the top its path. c) How long does it take to reach the top of its path? d) How fast is it traveling when it returns to Earth? e) Challenge: What is its maximum height? Additional Free Fall Review 1) If one had only a stopwatch, could one determine the initial speed of a ball launched vertically upward from the earth’s surface? Explain. 2) With only a stopwatch, could one determine how high the ball travels before it stops? Explain. Motion Graphs – Position vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating Motion Graphs – Velocity vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating Motion Graph Questions 1) What do you think might be happening in this graph? 2) What do you think position and velocity graphs of free fall motion might look like? Try to sketch them.

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posted: | 8/23/2011 |

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