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**Displacement and Velocity**

Honors Physics 4B - Finished

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**Biblical Reference John 20:4**

Both were running, but the other disciple outran Peter and reached the tomb first. John 20:4

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Representing Motion Physics is the study of the physical world, and the movement of objects is big part of the physical world. Start with 1 dimensional motion. (straight line) Describe motion in terms of motion diagrams. Develop a particle model to represent a moving object. Describe motion in terms of frame of reference, displacement, time, speed, and velocity. Calculate the displacement of an object traveling at known velocity for a specific time interval.

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Representing Motion Physics is the study of the physical world, and the movement of objects is big part of the physical world. Start with 1 dimensional motion. (straight line) Construct and interpret position vs. time graphs. Recognize the difference between scalar and vector. Distinguish the difference between instantaneous velocity and average velocity. Use motion equations to interpret graphs and solve motion problems.

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**Motion is RELATIVE How do you know if an object is moving?**

It depends completely on how you want to look at the moving object. You establish a frame of reference. A frame of reference allows you to measure the changes in position of an object. Example: You are sitting in an airplane which is moving at a speed of 100 km/h and there is a fly sitting on your head. What is your speed relative to the ground? What is your speed relative to the seat you're sitting in? What is the speed of the fly relative to you?

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Motion Diagram A Motion Diagram shows the position of an object at equal time intervals.

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Particle Model A Particle Model shows the position of an object in equal time intervals - the object is represented as a dot/particle

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Particle Model Here is the particle model of two toy cars. At any time in there motion, are they going the same speed?

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Coordinate System Coordinate Systems – provide more data about the motion diagram. (origin, direction, position, distance from the origin, displacement) The ball is moving in the positive x-direction.

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Scalar vs. Vector Scalar – a value without direction (Time, Mass, Distance) Vector – a value with direction. Resultant – The sum of two or more vectors. 4 m East

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**Displacement – Change in Position**

Not necessarily the total distance traveled. Displacement is relative to an axis. Distance is how far you have travelled regardless of direction. "x" displacement - moving horizontally either right or left. "y" displacement - moving vertically either up or down. Change is expressed using the Greek letter DELTA ( Δ ). Δx = xf - xi or Δy = yf - yi

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Example Suppose a person moves in a straight line from the lockers (at a position x = 1.0 m) toward the physics lab (at a position x = 9.0 m). The answer is positive. So the person must have been traveling horizontally to the right.

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**Example Suppose the person turns around!**

The answer is negative so the person must have been traveling horizontally to the left What is the DISPLACEMENT for the entire trip? What is the total DISTANCE for the entire trip?

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Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 2 4 6 Note: Displacement to the right is positive

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Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 2 4 6 Note: Displacement to the left is negative

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Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 2 4 6 Note: Displacement to the right is positive

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**Displacement A student walks 70 m East, then walks 30 m West.**

What is the magnitude of the students net displacement? A) 30 m B) 40 m C) 70 m D) 100 m East West 70 m 30 m Displacement 40 m

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**Position vs. Time Graphs**

Plots a moving objects position compared to its time. Position vs Time

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Motion Graphs An object starts from rest and moves with constant acceleration. 4 8 12 16 20 24 28 (s) x 4 8 12 16 20 24 28 (m) 1 2 3 t 5

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**Position vs. Time Graphs**

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Average Velocity Velocity (vector): The rate at which displacement changes. Rate = Any quantity divided by time. Speed (scalar): The rate at which distance changes.

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Example A football player runs 300. m in 1.50 min towards the far end of the field and then runs back to his starting point in min. What was the player’s average velocity (a) in running to the far end of the field (b) coming back to the starting point, and (c ) for the total run.

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**Slope – A basic graph model**

Look at the formula for velocity. What is the slope? What is the y-axis or the rise? What is the x-axis or the run? For a Displacement vs. Time graph, the velocity of an object during a specific time intervals is the slope. Velocity Displacement Time

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Motion Graphs The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s.

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Motion Graphs The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s.

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Motion Graphs The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s.

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Motion Graphs The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s.

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Motion Graphs The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s.

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**Slope Acceleration Graph**

x 4 8 12 16 20 24 28 (m) 1 2 3 t 5

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**Average Velocity Motion Equation #1**

di = -2 m Average velocity = 5.5 m/s y = mx + b y = (5.5m/s)x + -2m Equation of motion for average velocity d = vt + di

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Example A bicyclist travels at a constant speed of 4.0 m/s for 5.0s. How far does he go?

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Calculator Exercise Determine whether each set of data shows constant velocity or acceleration. Time (s) Distance (m) 5 1 7.1 2 12.8 3 23.2 4 36.9 Time (s) Distance (m) 5 1 7.1 2 8.9 3 11.2 4 13.1

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