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Chapter 10: Motion 10.1 An object in motion changes position 10.2 Speed measures how fast position changes 10.3 Acceleration measures how fast velocity changes

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Before, you learned: –Speed describes how far an object travels in a given time –Velocity is a measure of the speed and direction of motion Now, you will learn: –How acceleration is related to velocity –How to calculate acceleration

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Speed and direction can change with time Throw a ball in the air, it comes back down, bounces on the ground - the speed and direction are constantly changing You can find out an object’s position change during a certain amount of time if you know the velocity Can also measure how an object’s velocity changes with time: –Acceleration: The rate at which velocity change with time – how quickly velocity is changing –Constant 30 km/hr trip: acceleration = ?

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Acceleration Typically “speeding up”, but can be any change in velocity –A car slowing down is accelerating –A runner turning a corner, yet at constant speed, IS accelerating – direction of velocity has changed –A vector - size & direction…a change being slow down, speed up, or turn

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Acceleration 1. Acceleration in the same direction as motion –The speed of the object increases 2. Acceleration in the opposite direction of motion –The speed of the object decreases 3. Acceleration at a right angle to motion –The direction of motion changes (speed can stay the same)

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Acceleration can be calculated from velocity and time A race: in 1 s, you go from standing still to running 6 m/s, while your classmate goes from 0 m/s to 3 m/s –How did velocity change over time? Compare the initial and final velocities Know the time interval over which the velocity changed –Acceleration = ?? –What if classmate goes from 3 to 6 m/s in 1 s? –As long as the velocity is increased by 3 m/s, the acceleration remains the same.

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Calculating Acceleration Know the initial and final velocities, and the time interval Acceleration (m/s 2 ) = [final velocity (m/s) – initial velocity (m/s)] time (s) a = v final – v initial m/s 2 = ( m/s – m/s) = (m - m) * 1 t s s s s 1. A train traveling at 10 m/s slows down to a complete stop in 20 s. What is the acceleration of the train? 2. Man walking 0.5 m/s accelerates to 0.6 m/s in 1 s. You know: You want to know: Formula: Substitute: Calculate: Check your units:

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Calculating Acceleration Know the initial and final velocities, and the time interval Acceleration (m/s 2 ) = [final velocity (m/s) – initial velocity (m/s)] time (s) a = v final – v initial m/s 2 = m/s – m/s = (m - m) * 1 t s s s s A man walking 0.5 m/s accelerates to 0.6 m/s in 1 s. What is his acceleration? You know: You want to know: Formula: Substitute: Calculate: Check your units:

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Acceleration over Time Even a very small acceleration can lead to great speeds if given enough time –Deep Space 1: acceleration < 0.0002 m/s 2 over 20 months speed is increased by 4500 m/s (10,000 mi/h) –Although the thrust from the engine is less pressure than the weight of a single sheet of paper in the hand, each day it will add between 15 mph to 20 mph to the probe's speed. In 300 days it will have accelerated the Deep Space One by 60,000 mph

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Velocity-time graphs Acceleration = velocity / time The distance an object travels depends on its velocity

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Velocity Time Graph Calculate how far the ball traveled: Distance = velocity * time

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Velocity Time Graph Acceleration (m/s 2 ) = [final velocity (m/s) – initial velocity (m/s)] time (s) Question: Consider the motion of the object whose velocity-time graph is given in the diagram. 1.What is the acceleration of the object between times and ? 2.What is the acceleration of the object between times and ? 3.What is the net displacement of the object between times and ?

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