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Unit 1: Motion in One Dimension

Motion …

Kinematics in One Dimension

The source of content for this course is www.physicsclassroom.com

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Lesson Objectives

Students will be able to…• Analyze and evaluate Linear Motion by

Algebraic Means using the Kinematic equations

Lesson 4: 1-D Motion Algebra

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Motion Equations

vavg = average velocity (m/s)aavg = average acceleration (m/s2)Δd = df - di = displacement (m)Δt = tf - ti = time (s)Δv = vf - vi = velocity (m/s)

Lesson 4: 1-D Motion Algebra

t

dvavg

t

va avg

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Motion Equations

• Set of 4 equations• Used to predict unknown information about an

object's motion if other information is known• Only for motion with• constant velocity (an acceleration = 0 m/s2)• constant acceleration

Lesson 4: 1-D Motion Algebra

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Motion Formulas

vi = initial velocity (m/s)vf = final velocity (m/s)a = acceleration (m/s2)d = displacement (m)t = time (s)

Lesson 4: 1-D Motion Algebra

2i at2

1tvd t

2

vvd fi

What if the object starts from rest?

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Motion Formulas

vi = initial velocity (m/s)vf = final velocity (m/s)a = acceleration (m/s2)d = displacement (m)t = time (s)

Lesson 4: 1-D Motion Algebra

atvv if

What if the object starts from rest?

ad2vv 2i

2f

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Lesson 4: 1-D Motion Algebra

Problem Solving

7-Steps to Highly Effective Problem Solving -1. Construct an informative diagram

2. Identify given information in variable form

3. Identify unknown information in variable form

4. Identify equation which will be used

5. Substitute known values into the equation and solve

6. Show the answer with proper units and significant digits

7. Check your answer to insure it is reasonable and correct

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Problem Solving

Example 1: Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process.

Lesson 4: 1-D Motion Algebra

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Problem Solving

Example 2: Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period.

Lesson 4: 1-D Motion Algebra

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Problem Solving

Free-falling objects & kinematic equations1. Free fall object has acceleration of -9.8 m/s2

2. If object dropped, initial velocity (vi) is 0 m/s.

3. If projected straight up, it will slow as it rises.• At the peak trajectory, its velocity is 0 m/s. • Initial velocity is equal to final velocity

Lesson 4: 1-D Motion Algebra

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Problem Solving

Example 3: Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.

Lesson 4: 1-D Motion Algebra

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Problem Solving

Example 4: Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.

Lesson 4: 1-D Motion Algebra

Bonus:At what velocity does it hit Rex in the head?How long after throwing it does it hit Rex in the head?

Do Worksheet Problems: Motion Problems

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Summary

Problem Solving: Use “7-Steps to Success”

Lesson 4: 1-D Motion Algebra

2i at2

1tvd t

2

vvd fi

atvv if ad2vv 2i

2f