CN – Kinematic Graphs What is kinematics? 3 types of Kinematic Graphs

CN – Kinematic Graphs What is kinematics? –The study of objects in motion. We will look at three main graphs … 3 types of Kinematic Graphs –Distance vs. Time (d-t) –Velocity vs. Time (v-t) –Acceleration vs. Time (a-t)

Learning Objective To be able to measure and graph the motion of an object using a distance-time (d-t) graph.

Video on Train Motion Which train is in motion? How do you know?

1.How do you know when something is in motion? 2. How can you determine if you are moving forward or if everyone else is moving backwards? 3. For the train video which train is moving? How can you tell?

WU – Motion 1.How do you know when something is in motion? The position of object changes with time 2.How can you make everyone in the class move backwards? Walk forward (they appear to move backwards from your perspective) 3.How can I make everyone in the class move forward? Walk backwards ( they appear to move forward from your perspective)

WU – Pair-Share on Motion 4.How can you determine if you are moving forward or if everyone else is moving backwards? You can if you can observe a stationary reference point (ground). If you can’t see the ground then you will not know if you are moving or if they are!

1 st Rule of Motion The motion of an object is always measured relative to We usually use the ground as our

1 st Rule of Motion The motion of an object is always measured relative to another object or location. (The object or location used is called the frame of reference). We usually use the ground as our frame of reference.

What tools do we need to measure motion/speed? MeasurementsTools

What tools do we need to measure motion/speed? MeasurementsTools

What tools do we need to measure motion/speed? Tools Measurements

Kinematic Variables and Units 4 variables used to describe the motion of an object

Kinematic Variables and Units 4 variables used to describe the motion of an object

How can we make a graph to represent the motion of an object?

Distance vs. Time Graphs A car is measured to be at the following position at the following times: Time Position 0 s0 m 5 s 2 m 10 s4 m 15 s4 m 20 s0 m Using the data make a graph of Distance vs. Time (Time is always on the x-axis)

Distance vs. Time Graph for Car

What is the velocity of the car for parts A, B and C?

Describe the Motion of the Car in Words

End Day 1

CN - Describing Position-Time Graphs

Learning Objective To be able to describe the motion of an object using a distance-time (d-t) graph. Students will be able to determine the velocity of an object using a distance time graph.

Determine the slope of the Position Time Graph. What does the slope of a position time graph tell you?

Determine the slope of the Position Time Graph. What does the slope of a position time graph tell you?

Determine the slope of the Position Time Graph. What does the slope of a position time graph tell you?

Big Idea #1 The slope of a position time graphs gives the ______________________ Formulas:

Big Idea #1 The slope of a position time graphs gives the velocity of an object.

Describe the motion of the car in the graph. Be sure to include speed, direction and times where possible.

Describe the motion of the car in the graph. Be sure to include speed, direction and times where possible.

Describe the motion of each car. Describe what is happening at 3s in the graph.

End Day 2

CN – Velocity vs Time Graphs Given a Distance vs. time graph how can you make a velocity vs. time graph?

Learning Objectives To be able to make a velocity vs time (v-t) graph from a distance vs time (d-t) graph or table. To know that the slope of a distance vs time (d-t) graph gives the velocity.

How to Find the Velocity of a d-t graph 1.The slope of the d-t graph gives _________________ 2.To find the slope, pick two points called initial (t i, x i ) and final (t f, x f ) Formula 3. Slope of d-t graph = __________ =

Draw a Distance vs. Time and a Velocity vs Time graph for a slow walker (A), a fast walker(B) on the same graph. Assume they start from the same point! Slow walker: Walks slow at a constant speed. Fast walker: Walks fast at a constant speed. Distance vs Time Velocity vs Time

Draw a Distance vs. Time and a Velocity vs Time graph for a slow walker (A), a fast walker(B) on the same graph. Assume they start from the same point! Distance vs Time Velocity vs Time Slow walker: Walk slows at a constant speed. Fast walker: Walk fast at a constant speed.

Draw a Distance vs. Time and a Velocity vs Time graph for a slow walker (A), a fast walker(B) on the same graph. Distance vs Time Velocity vs Time Slow walker: Walk slows at a constant speed. Fast walker: Walk fast at a constant speed.

Draw a Distance vs. Time and a Velocity vs Time graph for a fast starter (C) and a fast finisher (D) on the same graph. Fast starter: Starts fast and then slows down. Fast finisher: Starts slow and than speeds up. Distance vs Time Velocity vs Time

Draw a Distance vs. Time and a Velocity vs Time graph for a fast starter (C) and a fast finisher (D) on the same graph. Fast starter: Starts fast and then slows down. Fast finisher: Starts slow and than speeds up. Distance vs Time Velocity vs Time

Draw a Distance vs. Time and a Velocity vs Time graph for a person that walks forward 10 m in 10s then turns around and walks back twice as fast. Distance vs Time Velocity vs Time

Draw a Distance vs. Time and a Velocity vs Time graph for a person that walks forward 10 m in 10s then turns around and walks back twice as fast. Distance vs Time Velocity vs Time

End Day 3

CN – Matching d-t to v-t graphs

Describe the motion for each d-t and v-t graph

Which v-t graph corresponds to the given d-t graph? Explain choice:

Which V-t graph corresponds to the given D-t graph? Explain choice:

New Idea: Curved d-t graphs Describe the motion shown in the graph?

Which v-t graph corresponds to the given d-t graph? Explain choice:

Which v-t Graph Corresponds to the Given d-t Graph? Explain choice:

End Day 4

CN – Acceleration from v-t Graphs

Warm-Up: Write a description of the motion shown in the graphs. velocity m/s

Answers to bell work The car is accelerating at m/s 2 from 0 s to 5 s. From 5 s to 10 s the car is at a constant speed of 25m/s.

Warm-Up: Determine the acceleration of the car for each segment. velocity m/s

Problem: Find the acceleration of the object shown in the graph velocity m/s m/s

Describe how you can find the acceleration given a v-t graph

How to find the Acceleration using a v-t graph 1.The slope of the v-t graph gives _________________ 2.To find the slope, pick two points called initial (t i, v i ) and final (t f, v f ) Formula 3. Slope v-t graph = ___________ =

Any straight line x-t graph means __________ _____________________________________ What does this look like? Straight Line x-t graphs Big Idea #1 x t x t x t

Any straight line x-t graph means __________ _____________________________________ What does this look like? Straight Line x-t graphs Big Idea #1 x t x t x t

Straight Line x-t Graphs Distance vs. Time Velocity vs. Time Acceleration vs. Time x (m) t (s) v (m/s) t (s) a (m/s 2 ) t (s) A C B Complete the v-t and a-t graphs below

Straight Line x-t Graphs Distance vs. Time Velocity vs. Time Acceleration vs. Time x (m) t (s) v (m/s) t (s) a (m/s 2 ) t (s) All STRAIGHT LINE x-t graphs have a constant velocity and zero acceleration! Why? The slope of the v-t graph gives the acceleration 1 slope = 1 velocity = no acceleration! Label different graphs using A, B and C or use lines with dots and dashes A A A C C C B B B Draw these three graphs on ½ sheet of paper with labels All zero slopea = 0 m/s 2

A curved (parabolic) x-t graph always means the object has a _______________________ ____________________________________ This means the object is ________________ _____________________________________ Curved x-t graphs The BIG Idea #2

A curved (parabolic) x-t graph always means the object has a changing velocity and acceleration is not zero! Object is speeding up or slowing down! Curved x-t graphs The BIG Idea #2

Curved Line x-t Graphs Distance vs. Time Velocity vs. Time Acceleration vs. Time x (m) t (s) v (m/s) t (s) a (m/s 2 ) t (s) A B Complete the v-t and a-t graphs below C

Curved Line x-t Graphs Distance vs. Time Velocity vs. Time Acceleration vs. Time x (m) t (s) v (m/s) t (s) a (m/s 2 ) t (s) AA A B B B All CURVED x-t graphs have a constant non-zero acceleration! Why? The slope of the v-t graph gives the acceleration! Positive slopea = + m/s 2 Negative slope a = - m/s 2

Big Ideas Summary The slope of an x-t graph gives the ___________. The slope of a v-t graph give the ____________. x-t graph v-t graph a-t graph

Big Ideas The slope of an x-t graph gives the velocity. The slope of a v-t graph give the acceleration x-t graph v-t graph a-t graph

B Last Set - Curved Line x-t Graphs Distance vs. Time Velocity vs. Time Acceleration vs. Time x (m) t (s) v (m/s) t (s) a (m/s 2 ) t (s) A Tip – Remember the slope of x-t gives v-t and the slope of v-t gives a-t Pair Share – Fill in the missing v-t and a-t graphs!

B Curved Line x-t Graphs Distance vs. Time Velocity vs. Time Acceleration vs. Time x (m) t (s) v (m/s) t (s) a (m/s 2 ) t (s) A A A B B All CURVED x-t graphs have a constant non-zero acceleration! Why? The slope of the v-t graph gives the acceleration! Positive slopea = + m/s 2 Negative slope a = - m/s 2

End Day 5

CN – All three Kinematic Graphs d-t, v-t and a-t

Acceleration Definition: Acceleration is the ___________ _____________________________________ Example: Determine the acceleration of a car that goes from 0 m/s (rest) to 24 m/s in 6 s. Units

Acceleration Definition: Acceleration is the increase or decrease of velocity over a period of time. Example: When you start running, you accelerate (increase your velocity) until you reach a constant speed. Units

Determine the acceleration using the v-t graph a (m/s 2 ) t

How do you find the acceleration from a V-t graph? a (m/s 2 ) t Why is this the answer?

VariableNameUnitsExample x t v a Review of Units for Variables

VariableNameUnitsExample x distance/ position lengthm, miles, km, ft t time s, min, hr, days v velocity/ speed a acceleratio n Review of Units for Variables

Acceleration Profiles 1 Object at rest. v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 1 Object at rest. v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 2 Object moving at a constant velocity. v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 2 Object moving at a constant velocity. v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 3 Object increasing in speed moving to the right (positive direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 3 Object increasing in speed moving to the right (positive direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 4 Object decreasing in velocity moving to the right (positive direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 4 Object decreasing in velocity moving to the right (positive direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 5 Object increasing in speed moving to the left (negative direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 5 Object increasing in speed moving to the left (negative direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 6 Object decreasing in speed moving to the left (negative direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Acceleration Profiles 6 Object decreasing in speed moving to the left (negative direction). v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

End Day 6

Dune Buggy Lab

Learning Objectives To be able to make a velocity vs time (v-t) graph from a distance vs time (d-t) graph or table. To know that the slope of a distance vs time (d-t) graph gives the velocity.

Procedure, Data Tables and a Diagram for Lab Must do at least 3 trials (can be on same course) Procedure must have 6 to 8 distance points per trial. Must have data tables with distance filled in! Must have a drawing of lab set up. You can work in groups of 3, must agree on procedures and I must sign off before you can take materials and do the lab

Be careful with cars! No jumping or dropping off any heights! Always start them on the ground Be gentle with on and off button. They tend to break if pushed too hard. If a car breaks the group is responsible ($10 per broken car) Only use the chalk to write on ground for distance. No names or marking anywhere else!

Behavior outside of class When you are doing the lab in the quad or hallways always remember to be use inside voices (no loud talking). Your group must have a pass to be outside the class.

After you take data 1.Take graph paper and lab questions on center desk (these are both due Thursday) 2.Work on making a Distance Vs. Time graph of your data. Use your average time. Make the graph at least ½ of graph paper or use front and back. Make a line of best fit through your data. 3.The slope of the distance vs. time graph gives the velocity of the car.

End Day 7

CN - Motion Diagrams

Motion Diagrams Show the _________________________ ___________________________________ Examples:

Motion Diagrams Show the location of an object with optional velocity and accelerations arrows at evenly spaced time intervals.

Examples of Motion Diagrams

Add the velocity and acceleration arrows to the motion diagrams shown below: Slide 1-8

Add the velocity and acceleration arrows to the motion diagrams shown below: Slide 1-8

Example 1: Motion Diagrams Alice is sliding at a constant velocity along a smooth, flat, iced lake on her skates when she suddenly slows down to a stop. Draw a motion diagram for Alice. Show and label all velocity vectors.

Example 1: Motion Diagrams Alice is sliding at a constant velocity along a smooth, flat, iced lake on her skates when she suddenly slows down to a stop. Draw a motion diagram for Alice. Show and label all velocity vectors.

Three motion diagrams are shown. Which is a dust particle settling to the floor at constant speed, which is a ball dropped from the roof of a building, and which is a descending rocket slowing to make a soft landing on Mars? 1. (a) is dust, (b) is ball, (c) is rocket 2. (a) is ball, (b) is dust, (c) is rocket 3. (a) is rocket, (b) is dust, (c) is ball 4. (a) is rocket, (b) is ball, (c) is dust 5. (a) is ball, (b) is rocket, (c) is dust

End Day 8

CN – PGFFS method and Kinematic Equations

The PGFFS Problem Solving Method 1.Draw a PICTURE (OPTIONAL) 2.List all GIVENS by writing the variable and the number it equals with units. 4. What FORMULAS can you use? Remember you can only have one unknown to solve a formula. 5. SOLVE for the unknown variable(s). x = 10 m v f = 5 m/s a = -2.5 m/s 2 3.What are you trying to FIND? List the variable with a question. v o = ?

Kinematic Variables

Kinematic Formulas Position time equation with acceleration Velocity time equation No time equation

Quiz Cards

Front of card Velocity Initials, period

Back of Card 1.Velocity = 2.Formula 3.Units

Front of card Acceleration Initials, period

Back of Card 1.Acceleration = 2.Formula 3.Units

Front of card Position-Time Equation Initials, period

Back of Position-Time Equation 1.Big Idea: 2. Formula: 3. Example:

Front of card Velocity Time Equation Initials, period

Back of Velocity-Time Equation 1.Big Idea: 2. Formula: 3. Example:

Front of card Position-Time Equation CN - Initials, period

Back of Position-Time Equation 1.Big Idea: 2. Formula: 3. Example:

Front of card No-Time Equation Initials, period

Back of No-Time Equation 1.Big Idea: 2. Formula: 3. Example:

End Day 9

Extra Slides

Bellwork: Sketch the d-t, v-t and a-t graph of the data. PositionTime 5 m0 s 10 m2 s 15 m4 s 20 m6 s 40 m8 s 60 m10 s 80 m12 s

v (m/s) t (s) x (m/s) t (s) a (m/s 2 ) t (s)

Kinematic Graphs Distance vs. Time Velocity vs. Time Acceleration vs. Time x (m) t (s) v (m/s) t (s) a (m/s 2 ) t (s) Complete the v-t and a-t graphs below