UNIT 1 MOTION

What do you think? If you walk from home to school, and then immediately return to your home. If the distance from your home to school is 15 m, what is your …. –Distance? –Displacement?

–What are some of the units we can measure displacement with? –What are some of the tools we use to measure displacement?

Distance or Displacement Distance – Distance – the amount of space between two objects or points Displacement – the overall change in position of an object.

Calculating Displacement To calculate the displacement of an object you must know the beginning and ending point. d = x f - x i d = displacement X f = final position X i = initial position

Sample Problem 1 Brendan walked from Walmart to his home, and there existed 300 m between the two. What is the… Brendan walked from Walmart to his home, and there existed 300 m between the two. What is the… –Distance? –Displacement?

Sample Problem 2 Miranda walked from School to Subway and back at noon. If 20m existed between the school and Subway, what is the …. –Distance? –Displacement?

Speed or Velocity? Speed – is a measurement that describes how far an object has moved in a certain period of time without indicating direction. Velocity – is a measurement that describes how far an object has moved in a certain period of time, while at the same time indicating direction

Velocity calculations use displacement Speed calculations use distance Both velocity and speed calculations use time. –Time – the duration between two events and is usually measured in seconds, minutes, or hours

Relating Velocity to Displacement and Time Average Velocity (v ave ) - is the overall displacement divided by the total time it took to travel The equation for average velocity is:

Instantaneous velocity – the velocity at which an object is traveling at a particular instant. – It is not affected by its previous velocity, or by how long the object has been moving. –The speedometer and radar gun were designed to measure instantaneous velocity.

Constant Velocity (uniform motion) – occurs when the velocity of an object remains the same over an extended period of time –E.g. Using Cruise Control on your car

Sample Problem 1 Keri bikes to school, a total displacement of m (SW). She has to slow down twice to cross busy streets, but overall the journey takes her 1080 seconds. What is Keri’s average velocity during the trip?

ANSWER 1 ∆d = m ∆t = 1080 s V ave = ? = 450 m/1080 s = 450 m/1080 s V av = m/s

Sample Problem 2 Laura is trying to predict the time required to ride her bike to the nearby beach. She knows the distance is 5000 m and, from other trips, that she can average about 5 m/s (E) including slowing down for climbing hills. Predict how long the trip will take.

Answer 2 ∆t = s

Sample Problem 3 Derek has a summer job helping with bison research. He notes that they graze (move and eat grass) at an average velocity of about 0.03 m/s (NW) for about s/d. What is the displacement, in meters, will the herd travel in two weeks (14 d)?

Answer 3 ∆d =

Homework Aaron is riding a cow at a velocity of m/s for a period of s. How far did Aaron travel? Sally is driving for s if she drove 5000 m what was her velocity?

Homework Questions 1 – 6 on page 358

Changing Units All final calculations in Physics should be in meters and seconds Unit Equivalence to 1 m Km 1000 m hm 100 m d 10 m m 1 m dm 0.1 m cm 0.01 m mm m Unit Equivalence to 1 s 1 day s 1 h s 1 min 60 s

Convert the following to the appropriate units: 1) 2 hours 2) 100 km 3) 7 cm 4) 5 min 5) 2 km/s 6) 10 m/h 7) 500 km/h

What do you do when you have two different velocities? In some problems you will be given more than one velocity (an initial velocity and a final velocity) In most cases your initial velocity is 0 and is not stated in the problem In other cases the initial velocity is given a concrete value due to the fact that the object is in motion at the beginning of the problem and the velocity is altered at some point (either faster or slower).

Two Velocities In situations where there are two velocities (and only displacement and time) in most cases we will use the following formula d = (v f + v i ) t 2 2 d = displacement v f = final velocity v i = initial velocity t = time

Sample Problem 1 Kristen is sitting at a red light in her red corvette. The light turns green and Kristen instantaneously guns the engine of her car. If 10 seconds later Kristen is traveling at a velocity of 90 km/h in a northern direction (in a 50 km/h speed zone) what is her displacement?

Answer d = (25 m/s + 0 m/s) 10s 2 d = 125 m

Sample Problem 2 Brendan and Amber are at Walmart looking for a video game. They are walking down the video game isle at a velocity of 0.5 m/s. They happen to spot Miss Cook at the store and they want to avoid her seeing them in the isle with the video games, so they quickly leave the isle traveling at a velocity of 0.9 m/s. If it only took Brendan and Amber 3 seconds to exit the isle, what was their displacement?

Sample Problem 3 Mike and Brandon are driving in Sussex at 60 km/h towards Apohauqui. Brandon spots a huge pothole in the road and slows down to a velocity of 20 km/h to drive through the pothole. If 30 seconds later the boys have driven over the pothole, what was their displacement from the time that Brandon first noticed the pothole?

Sample Problem 4 Jalise is walking towards the mall at a velocity of 0.4 m/s. She sees a 50% off sale sign in the window and starts running towards the store. If her final velocity is 1.3 m/s (she is wearing stilettos). If the displacement between the store and where she spotted the sign is 0.6 km, how long did it take her to reach the store.

Sample Problem 5 Colin and Corey are snowboarding at Poley Mountain. If at the top of the hill they are traveling at a velocity of 3 m/s and it takes them a total time of 2 minutes to reach the bottom of the hill, a displacement of 500 m. How fast were Colin and Corey traveling at the bottom of the hill?

Sample Problem 6 Sam is snowshoeing around the trail behind the school for gym class. Sam has never used snowshoes before but quickly picks up the technique. If Sam is traveling at a velocity of 0.6 m/s at the end of the trail and it took her a 20 minutes to travel the 1 km long route. What was Sam’s initial velocity?

Homework Jackson is driving towards the train station with a velocity of 30 m/s. If it takes Jackson 10 minutes to reach and stop at the train station how far did he travel. Sally is riding her bike to the local KFC. It takes Sally 10 min to reach KFC which is 4.7 km away. What is Sally’s initial velocity if she ends the trip with a velocity of 17 m/s.

Review of Variables in Graphing Independent Variable – the variable that changes over the course of an experiment in order to compare results. Dependent Variable – the variable that changes as a result to changes in your independent variable

Graphing Expectations The title of your graph must be placed at the top of your graph Label your x and y axis with the appropriate terms and units Label the end of your axis with either an x or y Pick an appropriate scale for your values

Displacement Time Graphs When observing or constructing a displacement time graph your time is always your independent variable (x-axis), while your displacement is your dependent variable (y-axis) The slope represents the velocity (the relationship between the dependent and independent variable) –The greater the velocity the larger the slope

How to Interpret Displacement Time Graphs Time (s) x y Displacement (m) In this graph the object is not in motion. How can you tell this from the graph?

How to Interpret Displacement Time Graphs Time (s) x y Displacement (m) In this graph the object is moving with a constant velocity. How can you tell this from the graph?

In this graph the velocity is not constant. How can you tell this from the graph? How would you calculate average velocity for this graph? Time (s) x y Displacement (m)

How to Interpret Displacement Time Graphs Time (s) x y Displacement (m) In this graph there is no velocity. How can you tell this from the graph?

How to Interpret Displacement Time Graphs Time (s) x y Displacement (m) In this graph you would solely use the values of x i and x f to determine the displacement of the object, in order to calculate velocity. Why?

How to construct a displacement time graph Plot your points using an appropriate scale along your x and y axis Chose two points from your line of best fit and use them to calculate the slope of the line (velocity)

Graphing displacement and time d (m) t (s)

Defining Acceleration Acceleration (a) – is the rate of change in velocity and is calculated by the ratio of the change in velocity (∆v) to the time interval (∆t) during which this change occurred. Constant Acceleration – the same change in speed (∆v) occurs in each equal interval of time (∆t) Average Acceleration (a av ) – is the average rate of change in velocity of an object.

Sample Problem 1 Dustin accelerates at an average rate of 2.5 m/s 2 for 1.5 s. What is his change in velocity at the end of 1.5s?

ANSWER 1 ∆v = a∆t ∆v = (2.5 m/s 2 )(1.5s) ∆v = 3.8 m/s

Sample Problem 2 Ryan M. is skateboarding down a hill and changes his velocity from rest to 1.9m/s. If the average acceleration down the hill is 0.40m/s 2, for how long was Ryan on the hill?

ANSWER 2 ∆t = ? a = 0.40 m/s 2 ∆v = 1.9 m/s ∆t =4.8 s

Homework 1.Shannon is driving through Tim Horton’s drive thru with an acceleration rate of 6 m/s 2 for 60 s. What was her velocity? 2.Josh and Sam are best friends who are skiing at Poley. If they start at the top of the hill with a velocity of 0 m/s and at the bottom they have a velocity of 10 m/s. If it takes them 50 s to get to the bottom of the hill what is their rate of acceleration? 3.Maddy is horse back riding down Main Street. Maddy wants to make the green light so she accelerates her horse at a rate of 0.5 m/s 2 to a velocity of 6 m/s. How long did this take Maddy?

Kimbo Slice is riding a tricycle from end of the octagon to the other. If it takes Kimbo Slice 500 s to cover the 12 m. What was Kimbo Slice’s acceleration?

Refining the Acceleration Equation Both the initial velocity v i and the final velocity v f affect your acceleration. ∆v = v f – v i The acceleration equation can now be written as:

Sample Problem 3 Kerrin is moving at 1.8m/s near the top of a hill. 4.2 s later she is traveling at 8.3 m/s. What is her average acceleration?

ANSWER 3 V i = 1.8 m/s ∆t = 4.2s V f = 8.3 m/s a = ? a = 1.5 m/s 2

Sample Problem 4 A bus with an initial velocity of 12m/s accelerates at 0.62 m/s 2 for 15 s. What is the final velocity of the bus?

V i = 12 m/s a = 0.62 m/s 2 ∆t = 15 s V f = ? V f = 21 m/s

Acceleration While Slowing Down Acceleration while slowing down is calculated in the same manner as acceleration while speeding up. The only difference is that the acceleration is represented with a negative sign. Acceleration while slowing down is calculated in the same manner as acceleration while speeding up. The only difference is that the acceleration is represented with a negative sign.

Sample Problem 5 In a race, a car traveling at 100km/h comes to a stop in 5.0 s. What is the average acceleration? V i = 100 km/h V f = 0 ∆t = 5.0 s a = ?

Homework Nick is walking down the street drinking pop with a velocity of 3 m/s. He sees a huge crack in the sidewalk and trips (spilling his pop). If the time between when he saw the crack and when he falls is 10 s. What was his rate of acceleration?

Calculating Acceleration when given a Displacement v f 2 = v i 2 + 2a ▲d v i 2 = v f 2 - 2a ▲d a = v f 2 – v i 2 2d 2d d = v f 2 – v i 2 2a 2a

Sample Problem 1 Justin is biking to the local swimming hole which is 20 km away. If he begins his trek traveling at a velocity of 15 km/h and he accelerates at a rate of 0.03m/s 2. What is Justin’s final velocity?

Sample Problem 2 Kerrin is moving at 1.8 m/s near the top of a hill. 40 m later she is traveling at 8.3 m/s. What is her average acceleration?

Sample Problem 3 Lindsay is traveling to Moncton with her friends to go shopping. If the car is initially traveling at a velocity of 45 m/s for 100 km. When they reach their destination they are traveling at a velocity of 0 m/s, what is the rate of acceleration?