1 D Motion Motion Equations Basic Velocity Equation
1 D Motion
Motion Equations Basic Velocity Equation Under Constant Acceleration Δd = ______ df - d o v = ___ Δt tf - t o Δv = ______ vf - vo a = ___ Δt tf - t o vf = vo + at Average Velocity Under Constant Acceleration vo + vf v = ______ 2 vf 2 = vo 2 + 2 aΔd 1 Δd = vot + __ at 2 2 vo + vf t Δd = _______ 2
Intro (Day 1 after reading) 1. What is speed? 2. What is velocity? 3. What is acceleration?
• Section 1 How do the concepts of speed and distance, and velocity and displacement relate to each other?
Equations relate things to each other displacement average velocity = ______ time
Equations can be simplified into symbols d v = __ t
• Mechanics is the branch of physics that describes motion. • Kinematics describes how objects move. This unit will focus on how objects move in straight lines (forward and backward).
Scalar vs. Vector • Scalars represent magnitudes only (number and unit). – How many slices of pizza did you eat? – How many steps are in front of the building? – The answer to these questions is a scalar quantity.
Scalar vs. Vector • Vectors represent a magnitude and a direction. I walked 14 paces North. – The magnitude in this case is _________. – The direction is __________.
Scalar vs. Vector • Vectors represent a magnitude and a direction. I walked 14 paces North. 14 paces – The magnitude in this case is _________. North – The direction is __________.
Vocabulary • Distance – (scalar) a measurement of space between two objects. (ex. 5 m) • Displacement – (vector) how far from where we started. (ex. 5 m, east) • Speed – (scalar) how fast something is moving. (ex. 25 m/s) • • Velocity – (vector) how fast we are moving in a direction. (ex. 25 m/s. south)
Problem Set #1 Are the following scalars or vectors? 1. 2. 3. 4. 4 meters east The object was 4 meters I had 6 donuts I ran 6 miles west of the river
Problem Set #1 Are the following scalars or vectors? 1. 2. 3. 4. 4 meters east The object was 4 meters I had 6 donuts I ran 6 miles west of the river (vector) (scalar) (vector)
Calculating with scalars • If you are asked for speed or distance • The equation is similar to the velocity equation distance speed = _____ time
Lets look at a problem with a scalar quantity Ex. 1 a Joan walks four blocks, turns around, and walks two blocks. She walks for 90 seconds. • How far did Joan walk? • (since direction does not matter, all movement adds up)
Lets look at a problem with a scalar quantity Ex. 1 a Joan walks four blocks, turns around, and walks two blocks. She walks for 90 seconds. • How far did Joan walk?
Lets look at a problem with a scalar quantity Ex. 1 b Joan walks four blocks, turns around, and walks two blocks. She walks for 90 seconds. • How fast did Joan walk? • (take total distance and divide it by time)
Lets look at a problem with a scalar quantity Ex. 1 b Joan walks four blocks, turns around, and walks two blocks. She walks for 90 seconds. • How fast did Joan walk?
• Before we get into any more detailed math you need to learn a bit more about adding vectors and the procedure for solving a physics problem
Adding Vectors • Direction matters when adding vectors • A man goes east 2 km and then west 1 km, what was his displacement (from origin)?
Adding Vectors • You must turn the direction into a sign in front of the number • Later, when you have your final answer you will take the sign and make it a direction again • Use this as a general guide • The x axis can only be added or subtracted from other x axis vectors • The y axis can only be added or subtracted from other y axis vectors
Adding Vectors (simple example) • A man goes east 2 km and then west 1 km, where did he end off? 2 km east becomes a d 1 of +2 km 1 km west becomes a d 2 of -1 km Now add the two vectors (d 1 + d 2)
Adding Vectors (simple example) • A man goes east 2 km and then west 1 km, where did he end off? 2 km east becomes a d 1 of +2 km 1 km west becomes a d 2 of -1 km Now add the two vectors (d 1 + d 2)
Adding Vectors (simple example) • A man goes east 2 km and then west 1 km, where did he end off? 2 km east becomes a d 1 of +2 km 1 km west becomes a d 2 of -1 km Then convert it back into a direction
Problem set #2 1. A dog walks 50 m East and then 23 m West. What is its displacement? 2. A bird has flown 850 km South for the winter when he realizes he as to go back because it is still summer. After traveling 320 km North, what is the birds displacement? 3. Mr. Holden starts pacing the room. He goes 3 meters North, 4 meters South, 5 meters North, then 1 meter South. What is his displacement?
Problem set #2 1. A dog walks 50 m East and then 23 m West. What is its displacement?
Problem set #2 2. A bird has flown 850 km South for the winter when he realizes he as to go back because it is still summer. After traveling 320 km North, what is the birds displacement?
Problem set #2 3. Mr. Holden starts pacing the room. He goes 3 meters North, 4 meters South, 5 meters North, then 1 meter South. What is his displacement?
Day 2 Intro • A person walks 5 m east for 2 s and another walks 10 m west for 1 s. 1. What is the Distance traveled? 2. What is the displacement after 3 seconds?
Lets look at the average velocity equation closer displacement average velocity = ______ time Δd = ______ d f - do v = ___ Δt t f - to
displacement average velocity = ______ time Δd = ______ d f - do v = ___ Δt t f - to v is velocity …………. . (mks unit m/s) d is displacement …. . . (mks unit m) t is time …. . . . (mks unit s) df is final displacement do is initial displacement tf is final time to is initial time
Δd = ______ d f - do v = ___ Δt t f - to This equation can be used many different ways Δd v = ___ Δt df - d o v = ______ tf - t o df - d o v = ______ Δt
Follow this process every time!!! • When solving a problem: 1. List the given information in a table 2. Identify the unknown. 3. Use the equation that contains the unknown, the given information, and no other variables. 4. Substitute. 5. Solve. 6. Include units on final answers.
Lets look at a problem with a vector quantity Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s displacement from start to finish?
Lets look at a problem with a vector quantity Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s displacement from start to finish?
Lets look at a problem with a vector quantity • What is Joan’s displacement from start to finish?
Lets look at a problem with a vector quantity • What is Joan’s displacement from start to finish?
Lets look at a problem with a vector quantity • What is Joan’s displacement from start to finish?
Lets look at a problem with a vector quantity • What is Joan’s displacement from start to finish?
Lets look at a problem with a vector quantity Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s average velocity?
Lets look at a problem with a vector quantity Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s average velocity?
Lets look at a problem with a vector quantity Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s average velocity?
Lets look at a problem with a vector quantity Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s average velocity?
Lets look at a problem with a vector quantity Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s average velocity?
• Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s average velocity if she walks an additional two blocks West?
• Ex. Joan walks four blocks East, then turns around and walks two blocks West. Joan walks for three minutes. • What is Joan’s average velocity if she walks an additional two blocks West?
Review question • Which quantities give more information, scalars or vectors?
• Which quantities give more information, scalars or vectors? • Scalars: magnitude • Vectors: magnitude and direction
Ex. If a car travels 500 m North and 250 m South in 1 minute, what is its: • • Distance traveled? Displacement from where it began? Speed? Velocity?
Ex. If a car travels 500 m North and 250 m South in 1 minute, what is its: • Distance traveled? • Displacement from where it began?
Ex. If a car travels 500 m North and 250 m South in 1 minute, what is its: • Speed?
Ex. If a car travels 500 m North and 250 m South in 1 minute, what is its: • Speed?
Ex. If a car travels 500 m North and 250 m South in 1 minute, what is its: • Velocity?
Ex. If a car travels 500 m North and 250 m South in 1 minute, what is its: • Velocity?
• Ex. 2 If one car travels 100 m East for 5 seconds and another car travels 80 m West for 4 seconds. What is the velocity of the cars?
• Ex. 2 If one car travels 100 m East for 5 seconds and another car travels 80 m West for 4 seconds. What is the velocity of each car?
• Average velocity describes the object’s velocity over a period of time. • Instantaneous velocity describes the object’s velocity at one instant in time.
• What would a cars speedometer read? Average velocity or Instantaneous velocity
• What would a cars speedometer read? Average velocity or Instantaneous velocity
• With all that you now know, can you define constant velocity?
• With all that you now know, can you define constant velocity? • Moving at a constant speed in a certain direction without acceleration. • Constant velocity means a= 0 m/s 2
Problem Set #3 1. 2. 3. 4. What is a scalar? What is a vector? What are two examples of scalars? What are two examples of vectors?
Day 3 Intro 1. A person walks 5 m east for 2 s and another walks 10 m west for 1 s. What is the: a. distance traveled b. displacement c. speed d. velocity
• Section 2 How do you apply the concept of acceleration to describing an object’s motion?
• Acceleration describes how an object’s velocity changes with respect to time. • • What is deceleration? Can a car move forward without accelerating? Can a car move backward without accelerating? Can a car move forward and accelerate? Can a car move backward and accelerate? Can a car move forward and decelerate? Can a car move forward and accelerate?
• Acceleration describes how an object’s velocity changes with respect to time. • What is deceleration? Slowing down in the direction of travel • • • Can a car move forward without accelerating? Can a car move backward without accelerating? Can a car move forward and accelerate? Can a car move backward and accelerate? Can a car move forward and decelerate? Can a car move forward and accelerate?
• Average acceleration equals the change in velocity divided by time. change in velocity acceleration = _________ change in time • Can you write this using symbols? • What are the appropriate units for acceleration?
• Unit for acceleration is m/s/s or m/s 2
• Acceleration can either be a positive or negative change in motion. If it is negative, then the object is decelerating (slowing down). • If an object has a velocity and acceleration in the positive direction, how will the object travel?
• What are 3 things in your car that can cause acceleration?
• What are 3 things in your car that can cause acceleration? • Gas petal • Break • Steering Wheel
Problem Set #4 • What does the following ask for or tell us about any of our variables? 1. How fast was it going? 2. How fast will it go? 3. Object Starts at rest? 4. Object slows down? 5. Object comes to a stop?
Problem Set #4 • What does the following ask for or tell us about any of our variables? 1. How fast was it going? 2. How fast will it go? 3. Object Starts at rest? 4. Object slows down? 5. Object comes to a stop?
• Ex 1: A car accelerates from a traffic light and increases its velocity form 0 m/s to 20 m/s in 5 seconds. What is its acceleration?
• Ex 1: A car accelerates from a traffic light and increases its velocity form 0 m/s to 20 m/s in 5 seconds. What is its acceleration?
• A car accelerates from a traffic light and increases its velocity form 0 m/s to 20 m/s in 5 seconds. What is its acceleration? • Ex: The same car then travels for 10 seconds at a constant velocity of 20 m/s. What is its average acceleration over that ten second period?
• A car accelerates from a traffic light and increases its velocity form 0 m/s to 20 m/s in 5 seconds. What is its acceleration? • Ex: The same car then travels for 10 seconds at a constant velocity of 20 m/s. What is its average acceleration over that ten second period?
• A car accelerates from a traffic light and increases its velocity form 0 m/s to 20 m/s in 5 seconds. What is its acceleration? • Ex: The same car then travels for 10 seconds at a constant velocity of 20 m/s. What is its average acceleration over that ten second period? What is the average acceleration over the entire 15 seconds?
• A car accelerates from a traffic light and increases its velocity form 0 m/s to 20 m/s in 5 seconds. What is its acceleration? • Ex: The same car then travels for 10 seconds at a constant velocity of 20 m/s. What is its average acceleration over that ten second period? What is the average acceleration over the entire 15 seconds?
• Ex: Finally, the car decelerates at 0. 5 m/s 2. How long will it take for the car to come to a complete stop?
• Ex: Finally, the car decelerates at 0. 5 m/s 2. How long will it take for the car to come to a complete stop?
Day 4 Intro 1. Mike can go from 0 m/s to 15 m/s in 5 seconds. What is Mike’s acceleration? 2. Mike decelerates from 15 m/s to rest at 4. 5 m/s 2. How long does this take Mike?
Section 3 How do I apply the equations for constant acceleration to problem solving? Note: Real-world acceleration/deceleration rates are variable. We simplify the problems and approximate their rates as uniform/constant. The following problems will assume uniform acceleration.
Remember to follow this process every time!!! • When solving a problem involving uniform acceleration: 1. List the given information in a table 2. Identify the unknown. 3. Use the equation that contains the unknown, the given information, and no other variables. 4. Substitute. 5. Solve. 6. Include units on final answers.
Note: • There may be more than one way to solve a problem. It’s important to work with consistent units. For example, if the displacement is measured in meters and the velocity is measured in km/hr, you will need to convert units.
Uniform acceleration equations vf = vo + at v 2 f = vo + 2 aΔd 2 1 Δd = vot + __ at 2 2 vo + v f t Δd = _______ 2 What does each variable stand for? ________ vf = vo = a= Δd = t=
Uniform acceleration equations vf = vo + at v 2 f = vo + 2 aΔd 2 1 Δd = vot + __ at 2 2 vo + v f t Δd = _______ 2 What does each variable stand for? ________ vf = vo = a= Δd = t= final velocity initial velocity acceleration displacement time
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration? • Write your givens and needs, then pick your equation
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration?
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration?
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration? Only one that is left
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration?
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration? • How much time did it take?
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration? • How much time did it take?
• Ex. A car accelerates from rest to a final speed of 40 m/s in 100 m. What is the car’s acceleration? • How much time did it take?
• Ex. 2 A car traveling at 25 m/s accelerates at 5 m/s 2 for 5 seconds. How far does the car travel?
• Ex. 2 A car traveling at 25 m/s accelerates at 5 m/s 2 for 5 seconds. How far does the car travel?
• Ex. 2 A car traveling at 25 m/s accelerates at 5 m/s 2 for 5 seconds. How far does the car travel?
• Ex. 2 A car traveling at 25 m/s accelerates at 5 m/s 2 for 5 seconds. How far does the car travel?
• Ex. 2 A car traveling at 25 m/s accelerates at 5 m/s 2 for 5 seconds. How far does the car travel? • What is its final velocity?
• Ex. 2 A car traveling at 25 m/s accelerates at 5 m/s 2 for 5 seconds. How far does the car travel? • What is its final velocity?
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