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Distance and Displacement Speed and Velocity Acceleration

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* (I) Choosing a Frame of Reference * To describe motion accurately and completely, a frame of reference is necessary * It is a system of objects that are not moving with respect to one another.

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* How Fast Are You Moving? * There are many correct answers because their motion is relative. * Relative motion * It is movement in relation to a frame of reference.

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* What is Distance? * It is the length of a path between two points. * What is Displacement? * It is the direction from the starting point and the length of a straight line from the starting point to the ending point.

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* What is a vector? * It is a quantity that has magnitude and direction * Magnitude can be size, length, or amount. * Vector addition is the combining of vector magnitudes and directions. * Add displacements using vector addition.

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* When two displacement, represented by two vectors, have the same direction, you can add their magnitudes. * Look at Figure 3 on page 330 * When two or more displacement vectors have different directions, they may be combined by graphing. * Look at Figure 4 on Page 331 * Resultant vector is the vector sum of two or more vectors.

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Quick lab: Comparing Distance and Displacement Procedure 1.Draw a dot at the intersection of two lines near the bottom edge of a sheet of graph paper. Lab the dot “Start” 2.Draw a second, similar dot near the top of the paper. Label this dot “End”. 3.Draw a path from the Start dot to the End dot. Choose any path that starts on the grid lines. 4.Use a ruler to determine the distance of your path. 5.Use a ruler to determine the displacement from start to end. Analyze and Conclude 1.Observing: Which is shorter, the distance or the displacement. 2.Evaluating and Revising: How could you have made the distance shorter? 3.Inferring: If you deep the Start and End points the same, is it possible to make the displacement shorter? Explain your answer. 11. 1 Distance and Displacement

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Section 11.1 Assessment Reviewing Concepts 1.A frame of reference is a set of objects that are not moving with respect to one another. 2.Distance is the length of an object’s actual path from a starting point to an ending point. Displacement is the length of a straight line from the starting point to the ending point. 3.Displacements are combined using vector addition. 4.If the plane is far away and flying directly toward or away from the girl, the plane would appear not to be moving. Also, the plane would not be moving in the frame of reference of the people on the plane. 5.Displacement is more like the length of a rope that is pulled tight; it measures the shortest distance between two points. 6.It makes sense to measure the height of a building in meters. Kilometers are too large and centimeters are too small. 7.You should use displacements. Displacements will tell your friend how far and which direction to go. Distances will only tell how far to go. 8.The vectors are at an angle to each other.

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* What is Speed? * It is the ratio of the distance an object moves to the amount of time the object moves. * What is average speed? * It is computed for the entire duration of a trip. * It is total distance divided by total time.

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* What is Instantaneous Speed? * It is the rate at which an object is moving at a given moment in time.

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* A distance-time graph is good way to describe motion. * Recall that slope is the change in the vertical axis value divided by the change in the horizontal axis value. * The slope of a line on a distance-time graph is speed!

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* What is velocity? * It is a description of both speed and direction of motion. * It is vector! * A longer vector would represent a faster speed, and a shorter one would show a slower speed. * A change in velocity can be the result of a change in speed, a change in direction, or both.

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* Sometimes the motion of an object involves more than one velocity. * Two or more velocities add by vector addition.

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Section 11.2 Assessment 1.Velocity describes both speed and direction 2.The slope of a line on a distance-time graph is equal to speed. 3.Average speed is calculated for the entire duration of a trip, whereas instantaneous speed is determined at a single moment. 4.Two or more velocities can be combined by vector addition. 5.A speedometer measures speed at the current moment, so it shows instantaneous speed, not average speed. Because a speedometer does not show direction it does not show velocity. 6.Students may describe how they could use a stopwatch to measure the time for the car to travel down the incline. The average speed would be calculated by dividing the distance traveled by the total time. 7.Slope is equal to the change in vertical value divided by the change in horizontal value. On a distance-time graph, the change in vertical value is a distance and the change in horizontal value is a time. Therefore, the slope is distance divided by time, which equals average speed. 8.V = (50.0 m)/23.1 s) = 2.16 m/s 9.D = v x t = (600 km/h)(2.5 h) = 1500 km

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* 1. What is Acceleration? * It is the rate at which velocity changes. * It can be described as changes in speed, changes in direction, or changes in both. * It is a vector.

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* What is free fall? * The movement of an object toward Earth solely because of gravity. * Gravity = 9.8 m/sec 2 * You can accelerate even if your speed is constant. * Although you may have a constant speed, your change in direction means you are accelerating.

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* You experience this type of motion if you ride on a roller coaster like the one in Figure 14 on Page 344. * Your acceleration is constantly changing because of changes in the speed and direction of the cars of the roller coaster. * What is constant acceleration? * It is a steady change. * It is the velocity of the object changes by the same amount each second.

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* Calculating Acceleration * Acceleration is the rate at which velocity changes. * You calculate acceleration for straight-line motion by dividing the change in velocity by the total time. * A = (v f – v i )/t

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* Math Skills * A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball? * List your information * Show your formula * Substitution of values * Solve for your unknown * 3 m/s 2 down the ramp

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* Math Practice * 1. A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. What is its acceleration (deceleration)? * A = (0 – 10)/20 = -.5 m/s 2 * 2. An airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s 2. What is it s change in velocity during this time? * (v f – v i ) = 9.0 x 4 = 36 m/s

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* 3. A child drops a ball from a bridge. The ball strikes the water under the bridge 2.0 seconds later. What is the velocity of the ball when it strikes the water? * V f = 0 + (9.8 x 2) = 19.6 m/s * 4. A boy throws a rock straight up into the air. It reaches the highest point of its flight after 2.5 seconds. How fast was the rock going when it left the boy’s hand? * V i = 0 – (9.8 x 2.5) = -25 m/s

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* The slope of a speed-time graph is acceleration. * This slope is change in speed divided by change in time. * Speed increased at a constant rate

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* Constant negative acceleration decreases speed. * Accelerated motion is represented by a curved line on a distance-time graph.

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* Acceleration is rarely constant. * Motion is rarely in a straight line. * Instantaneous acceleration is how fast a velocity is changing at a specific instant. * You should begin to study!

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* Section 11.3 Assessment * 1. Changes in velocity can be described as changes in speed, changes in direction, or changes in both (or, an increase in speed, a decrease in speed, or a change in direction). * 2. a = (v f – v i )/t * 3 The slope of the line on a speed-time graph gives the acceleration. * 4. Instantaneous acceleration is how fast the velocity is changing at a specific instant.

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* 5. Deceleration is a special case of acceleration in which the speed of an object is decreasing. * 6. Train B = 8.0 + (1.0 x 10.0) = 18 m/s * 7. The graph indicates that the object is accelerating.

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* 8. a = (25 – 0)/30 = 0.83 m/s 2 * 9. (30 -25)/10 = 0.5 m/s 2 * Time for Test!!!!!!!

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