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Kinematics – Defining Motion Unit #2 Kinematics

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Objectives and Learning Targets Understand the difference between distance and displacement and between speed and velocity. Calculate distance, displacement, speed, velocity, and acceleration. Solve problems involving average speed and average velocity. Unit #2 Kinematics

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Defining Motion Position - refers to an objects location at any given point in time. Position is a vector, and its magnitude is given by the symbol x. Distance – is how far an object travels (in one dimension at a type) from its initial position. Distance is a scalar. It has a magnitude, or size, only. The basic unit of distance is the meter (m). Unit #2 Kinematics

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Sample Problem #1 On a sunny afternoon, a deer walks 1300 meters east to a creek for a drink. The deer then walks 500 meters west to the berry patch for dinner, before running 300 meters west when startled by a loud raccoon. What distance did the deer travel? Unit #2 Kinematics

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Sample Problem #1 On a sunny afternoon, a deer walks 1300 meters east to a creek for a drink. The deer then walks 500 meters west to the berry patch for dinner, before running 300 meters west when startled by a loud raccoon. What distance did the deer travel? Answer: The deer traveled 1300m + 500m + 300m, for a total distance traveled of 2100m. Unit #2 Kinematics

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Displacement Different from distance, displacement – is how far an object is from its starting point, or its change in position. The vector quantity displacement Δx = (x-x 0 ) describes how far an object is from its starting point, and the direction of the displacement vector points from the starting point to the finishing point. Like distance, the units of displacement are meters (m). Unit #2 Kinematics

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Sample Problem #2 A deer walks 1300 m east to a creek for a drink. The deer then walked 500 m west to the berry patch for dinner, before running 300 m west when startled by a loud raccoon. What is the deer’s displacement? Unit #2 Kinematics

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Sample Problem #2 A deer walks 1300 m east to a creek for a drink. The deer then walked 500 m west to the berry patch for dinner, before running 300 m west when startled by a loud raccoon. What is the deer’s displacement? Answer: The deer’s displacement was 500m east. Unit #2 Kinematics

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Sample Problem #3 Unit #2 Kinematics

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Sample Problem #3 Unit #2 Kinematics

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Speed and Velocity Knowing only an object's distance and displacement doesn't tell the whole story. Going back to the deer example, there's a significant difference in the picture of the deer's afternoon if the deer's travels occurred over 5 minutes 300 seconds) as opposed to over 50 minutes (3000 seconds). How exactly does the picture change? In order to answer that question, you'll need to understand some new concepts – average speed and average velocity. Average speed, given the symbol, is defined as distance traveled divided by time, and it tells you the rate at which an object's distance traveled changes. When applying the formula, you must make sure that x is used to represent distance traveled. Unit #2 Kinematics

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Sample Problem #4 A deer walks 1300 m east to a creek for a drink. The deer then walked 500 m west to the berry patch for dinner, before running 300 m west when startled by a loud raccoon. What is the deer's average speed if the entire trip took 600 seconds (10 minutes)? Unit #2 Kinematics

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Sample Problem #4 A deer walks 1300 m east to a creek for a drink. The deer then walked 500 m west to the berry patch for dinner, before running 300 m west when startled by a loud raccoon. What is the deer's average speed if the entire trip took 600 seconds (10 minutes)? Answer: Unit #2 Kinematics

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Average Velocity Average velocity, also given the symbol, is defined as displacement, or change in position, over time. It tells you the rate at which an object's displacement, or position, changes. To calculate the average velocity, you divide the displacement by time (remember it’s a vector) Unit #2 Kinematics

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Sample Problem #6 A deer walks 1300 m east to a creek for a drink. The deer then walked 500 m west to the berry patch for dinner, before running 300 m west when startled by a loud raccoon. What is the deer's average velocity if the entire trip took 600 seconds (10 minutes)? Unit #2 Kinematics

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Sample Problem #6 A deer walks 1300 m east to a creek for a drink. The deer then walked 500 m west to the berry patch for dinner, before running 300 m west when startled by a loud raccoon. What is the deer's average velocity if the entire trip took 600 seconds (10 minutes)? Answer: Unit #2 Kinematics

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Avg. Speed vs. Avg. Velocity Notice how the answers for each are vastly different, the main reason is because distance and speed are scalars; while displacement and velocity are vectors. A good way to memorize is … Speed = Scalar Velocity = Vector Unit #2 Kinematics

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Sample Problem #7 Chuck the hungry squirrel travels 4m east and 3m north in search of an acorn. The entire trip takes him 20 seconds. Find: Chuck’s distance traveled, Chuck’s displacement, Chuck’s average speed, and Chuck’s average velocity. Unit #2 Kinematics

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Sample Problem #7 Chuck the hungry squirrel travels 4m east and 3m north in search of an acorn. The entire trip takes him 20 seconds. Find: Chuck’s distance traveled, Chuck’s displacement, Chuck’s average speed, and Chuck’s average velocity. Answer: Unit #2 Kinematics

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Acceleration What would happen if velocity never changed? Objects would move at the same speed and direction having the same kinetic energy and momentum. Acceleration – the rate at which the velocity of an object changes Unit #2 Kinematics

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Acceleration This indicates that the change in velocity divided by the time interval gives you the acceleration Acceleration is a vector – it has a direction the units of acceleration are meters per second per second, or [m/s 2 ] the units mean is that velocity changes at the rate of one meter per second, every second an object starting at rest and accelerating at 2 m/s 2 would be moving at 2 m/s after one second, 4 m/s after two seconds, 6 m/s after 3 seconds, and so on Special note is the symbolism for v. The delta symbol ( ) indicates a change in a quantity, which is always the initial quantity subtracted from the final quantity. For example: Unit #2 Kinematics

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Sample Problem #8 Monty the Monkey accelerates uniformly from rest to a velocity of 9 m/s in a time span of 3 seconds. Calculate Monty's acceleration. Unit #2 Kinematics

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Sample Problem #8 Monty the Monkey accelerates uniformly from rest to a velocity of 9 m/s in a time span of 3 seconds. Calculate Monty's acceleration. Answer: Unit #2 Kinematics

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Rearranging Acceleration The definition of acceleration can be rearranged to provide a relationship between velocity, acceleration and time as follows: Unit #2 Kinematics

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Sample Problem #9 The instant before a batter hits a kilogram baseball, the velocity of the ball is 45 meters per second west. The instant after the batter hits the ball, the ball's velocity is 35 meters per second east. The bat and ball are in contact for 1.0×10 -2 second. Determine the magnitude and direction of the average acceleration of the baseball while it is in contact with the bat. Unit #2 Kinematics

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Sample Problem #9 Answer: Unit #2 Kinematics

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+ and - Accelerations Because acceleration is a vector and has direction, it's important to realize that positive and negative values for acceleration indicate direction only. Take a look at some examples… rs_motion.html rs_motion.html Be careful with + and – vectors. A + accelerations does not always mean moving to the right, or a – mean moving left See Phet examples Unit #2 Kinematics

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