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**Physics Ch. 3 Position, Speed, and Velocity**

Motion (in 1 –D) Physics Ch. 3 Position, Speed, and Velocity

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MOTION Motion is a change in the position of a body or system with respect to time. Position is the location of a body or system at a given time. Motion can be mapped by a coordinate system. Coordinate Systems show the original location of the body (it’s initial or zero point) and the direction in which the body moves. North, Up, (+) West, Left, Backward,(-) East, Right, Forward,(+) South, Down, (-)

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**DISPLACEMENT vs. DISTANCE**

Distance is the total length an object traveled. It is a scalar quantity, which means it only has magnitude. (Magnitude refers to the amount) Displacement is the change in position of an object. It is a vector quantity, which means it has magnitude & direction. Objects at rest have a displacement of zero. Displacement is NOT the same as the distance traveled.

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**Example: A man traveled from point A to B to C to D.**

What is his displacement? He is back in his original position. A to B is 4m east C to D is 4m west→ 0 m they cancel each other out! B to C is 2m south D to A is 2m north → 0m What is his distance? 4m + 2m + 4m + 2m = 12m

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**Equation for Displacement**

∆d = df – di d stands for position f is for final position i is for initial position Draw a picture of the situation. Set-up your problem using two-column format List your givens & Equation: Show all work df = 10 m di = 5 m ∆d = ? ∆d = df – di ∆d = 10 m – 5 m ∆d= 5 m

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**Sample Problems Example #1:**

If the starting position of an object is 50 m west and the final position is 150 m east, what is the displacement? Example #2: If the starting position is 200 m north and the final position is 75 m south, what is the displacement?

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VELOCITY Velocity: the quantity that measures how fast something moves from one point to another -or- How fast you can move in a specific direction. Average Velocity: the total displacement divided by the time interval during which displacement occurred. Instantaneous Velocity: The speed and direction of an object at a particular instance in time.

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**Speed Vs. Velocity Speed is a SCALAR quantity – it has only magnitude**

Average speed is the distance traveled divided by the time interval. Velocity is a VECTOR quantity – it has magnitude & direction. Average Velocity is the displacement of an object divided by the time interval. SPEED VELOCITY

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Equations SPEED VELOCITY

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**Problem Solving RULES:**

Must draw a picture (motion diagram) that includes vector arrows representing speed/velocity and direction. Two Column Format: Left Side - Make a list of your given and unknowns, write the equation. Right Side - input your numbers (with units) into the equation, show how to solve the problem, box in your final answer.

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**Velocity & Speed Practice**

Joe and Sue take a 45 minute walk along a straight road to a store 3.0 km away. What is their average speed in m/s? A bus traveled on Newburgh Road from a bus stop on 8 mile south to a stop at 5 mile in 15 minutes (lucky for the bus all of the lights were green!). What is the bus’s average velocity? Smitty drives his car with an average velocity of 24 m/s toward the east. How long will it take him to drive 560 km on a perfectly straight highway.

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MOTION Diagrams A motion diagram (or map) represents the position, velocity, and acceleration of an object at various clock readings. Arrows called vectors are used to indicate the direction and magnitude of the object in motion. V V V V V

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Velocity & P-T Graphs You can determine the velocity of an object by finding the slope of position vs. time. Slope = change in vertical coordinates (y axis) change in horizontal coordinates (x axis) Slope = 30 m – 10 m = 20 m = 10 m/s 3 s – 1 s s Time (s) Position (m) 1 10 2 20 3 30 4 40 5 50

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3.2 Position time graph A position versus time graph shows a more detailed history of the drive, including when the car was moving, and when it was stopped. The graph shows that during the first hour, your position gradually increased from your initial position (0 miles) to a point 60 miles away. It then shows that you were stopped between 1 hour and 1.5 hours because your position didn’t change. Finally, the graph shows that you started driving again at 1.5 hours and changed your position until you reached a point 90 miles away from your starting point. The graph contains much more information because it shows the instantaneous speed all through the trip.

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**3.2 Interpret a position time graph**

The position versus time graph shows a boat traveling through a long canal. The boat has to stop at locks for changes in water level. a) How many stops does the boat make? b) What is the boat’s average speed for the whole trip? c) What is the highest speed the boat reaches? A position versus time graph shows a more detailed history of the drive, including when the car was moving, and when it was stopped. The graph shows that during the first hour, your position gradually increased from your initial position (0 miles) to a point 60 miles away. It then shows that you were stopped between 1 hour and 1.5 hours because your position didn’t change. Finally, the graph shows that you started driving again at 1.5 hours and changed your position until you reached a point 90 miles away from your starting point. The graph contains much more information because it shows the instantaneous speed all through the trip.

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Constant Speed On this graph, a constant speed is a straight horizontal line.

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**Application: Slow-motion Photography**

A video camera does not photograph moving images. It takes a sequence of still images called frames and changes them fast enough that your brain perceives a moving image. You can use an ordinary video camera to analyze motion in laboratory experiments.

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**Stop action photography is cool.**

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**Graphs -Position-time**

Straight line = constant speed. Slope tells velocity. (v = ∆d/∆t) Positive slope is positive velocity (going forwards) Negative slope is negative velocity (going backwards) Horizontal line = zero slope = stopped Change in slope means change in speed.

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**Graphs -Velocity-time**

Horizontal line = constant speed (velocity) Curved line = change in velocity (not constant) Straight line (not horizontal) = constant change in velocity Slope tells change in velocity Positive slope = constant acceleration (speeding up) Negative slope = constant acceleration (slowing down) Area under curve = distance travelled (v x t = d) m/s x s = m (when horizontal); ½ v x t =d (when sloped) Instantaneous velocity is tangent to curve at any point. Avg velocity is found between two points.

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