Tues. Feb. 18 Do NOW What is the difference between an independent variable and a dependent variable? Give an example of each. Do lab activity with CPO timers and photogates.

Wednesday, Feb. 19 DO NOW What metric (SI) units do we use to describe: 1- distance 2- time 3- mass 4- speed

The / sign means divided by or per. Speed Speed is the rate at which an object moves across a distance per unit of time. Speed = Distance /Time The / sign means divided by or per. The units in which speed is measured include any units of length or distance divided by any unit of time.

Units of speed Examples of units of speed include: -miles/hour -meters/second -feet/second -kilometers/hour Your textbook will usually use the units of meters per second (m/s) for speed.

If you ride a bike a distance of 5 meters in 1 second, what is your speed? If you ride a bike a distance of 10 meters in 2 seconds, what is your speed? If you ride a bike a distance of 100 meters in 20 seconds, what is your speed?

Instantaneous Speed- The speed at a given instant in time Instantaneous Speed- The speed at a given instant in time. Example: You are driving down the road. Your speedometer reads 25 mph. 25 mph is your instantaneous speed. The speed you see on a car speedometer is an instantaneous speed.

Average Speed Average speed – total distance covered/time interval Average speed does not tell you anything about your maximum or minimum speed. Example: If you travel 240 km in 4 hours, your average speed is 240 km/4 hr = 60 km/hr

You are driving 200 km to a concert in Madison You are driving 200 km to a concert in Madison. At one point you look at your speedometer and see that it reads 100 km/hr. You arrive at the concert in 2 hours. -What was your average speed? -What was your instantaneous speed at one point on your trip?

Speed vs. Velocity Speed is a description of how fast an object moves. Velocity is a description of how fast and in what direction an object moves. Velocity is speed with direction.

Examples of Velocity Measurements: -50 km/hr north -20 ft/s left -45 m/s southeast (SE) Does a car speedometer read speed or velocity? How do you know?

Constant Velocity Constant velocity requires constant speed AND constant direction. If an object is moving in a circular path at a constant speed, it is NOT moving with constant velocity because its direction is changing.

An object whose direction or speed is changing is moving with a changing velocity. Homework: Read Sec. 2.2 & 2.3 pg.11-14 Do problems 2-8 on page 25 and problem 26 on page 26

Thurs. Feb. 20 DO NOW Is the movement described below constant or changing velocity? 1-a child riding on a Ferris wheel at a constant speed; 2-a car driven at constant speed down Silver Spring Rd; 3-a student walking down stairs at a constant speed; 4-birds flying south for the winter; 5-Ms. Bandoian as she walks around the classroom?

Acceleration – the rate at which velocity is changing over time Acceleration = change in velocity time interval

Acceleration is the rate at which velocity (speed) changes. If your speed increases by 1 m/s each second, then your acceleration is 1 m/s per second. What is the acceleration for the steeper hill?

Speed and acceleration Speed and acceleration are not the same thing. Acceleration is the change in speed divided by the change in time.

Solving Problems A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 s. Calculate acceleration.

Solving Problems Looking for: acceleration of sailboat Given: vstart =1 m/s; vfinish = 4 m/s; time =3 s Relationships: a = vfinish – vstart/t Solution: a = (4 m/s – 1 m/s)/ 3 s = 1 m/s2

Speed and acceleration An acceleration in m/s/s is often written as m/s2 (meters per second squared). It is better to think about acceleration in units of speed change per second (that is, meters per second per second).

Acceleration is positive when velocity is increasing, for example when a car is speeding up. Acceleration is negative when velocity is decreasing, for example when a car is slowing down. Negative acceleration is called deceleration.

Acceleration can be happening even if the speed of an object is not changing. Remember, velocity consists of speed and direction. If the direction of motion is changing but the speed remains the same, the object is accelerating.

Acceleration and Direction Acceleration occurs whenever there is a change in speed, direction, or both.

Practice Problem: As a shuttle bus comes to a normal stop, it slows from 9.00m/s to 0.00m/s in 5.00s. Find the average acceleration of the bus.

Practice: a) A ball is dropped off a bridge Accelerating? Yes No Speed? Increase / Decrease / Neither   b) A man is running at a constant speed

Homework: Read pg. 15-16 Pg. 25 Review Questions 9-11 Pg. 26 Probs. 27, 28

Fri. feb. 21 DO NOW Write the formula for acceleration. Rearrange the formula so that t is the subject: d = ½ gt2

Reaction time activity

Monday, Feb. 24 DO NOW 3- Centi- means _________. 1-Describe a situation when acceleration is positive. 2-Describe a situation when acceleration is negative. 3- Centi- means _________. 4- One meter = _____ centimeters 5- One centimeter = ___ millimeters 6- A millimeter is what fraction of a centimeter? ____________ 7- One kilometer = _____meters 8- Kilo- means _________.

Review of speed, velocity, & acceleration Instantaneous Speed = speed at a given instant Average Speed = the total distance traveled divided by the total time of travel

Velocity is speed with direction. Speed is a description of how fast an object moves. Velocity is a description of how fast and in what direction an object moves. Velocity is speed with direction. Constant velocity requires constant speed AND constant direction. If an object is moving in a circular path at a constant speed, it is NOT moving with constant velocity because its direction is changing.

Acceleration – the rate at which velocity is changing over time Acceleration = change in velocity time interval

It is often useful to look at data on graphs. This is true of data on velocity and acceleration so we will do a review of graphing.

Line Graph A line graph is a graph that uses line segments to connect data points and show changes in data.

Graphs show relationships A good way to show a relationship between two variables is to use a graph. A graph makes it easy to see if changes in one variables cause changes in the other variable. Graphs help us see a cause & effect relationship.

The position vs. time graph To graph data, you put position on the vertical (y) axis Dependent variable Time goes on the horizontal (x) axis. Independent variable

The position vs. time graph An object moving at a constant speed always creates a position vs. time graph that is a straight line.

Slope You can use position vs. time graphs to quickly compare the speeds of different objects. A steeper line on a position vs. time graph means a faster speed.

Slope The “steepness” of a line is called its slope. The rise is equal to the height of the triangle. Change in Y-axis value The run is equal to the length along the base of the triangle. Change in X-axis value

The slope is equal to the rise divided by the run. The slope for position vs. time graph is therefore distance (position) divided by time. Which equals WHAT? Slope

Practice: How far did runner B travel in 100 seconds? How far did runner A travel in 100 seconds? Who was traveling at a faster speed?

Practice Continued: Calculate the average speed of runner A (total distance ÷ total time)   Calculate the average speed of runner B (total distance ÷ total time)

* 07/16/96 Graphing Motion slope = steeper slope = Straight line = flat line = Single point = instantaneous speed speed A B faster speed constant speed no motion *

Who had a constant speed? A Describe B from 10-20 min. Graphing Motion Who started out faster? A (steeper slope) Who had a constant speed? A Describe B from 10-20 min. B stopped moving Find their average speeds. A = (2400m) ÷ (30min) A = 80 m/min B = (1200m) ÷ (30min) B = 40 m/min A B

Do practice problems on your note sheet Do practice problems on your note sheet. Any not completed in class are homework!

Tues. Feb. 25 DO NOW Use a ruler to graph the following points on a sheet of paper from the wire tray on the front table. x y 0 -3 5 17 -2 -11 1 1 Draw a line between the points.

* 07/16/96 Graphing Motion slope = steeper slope = Straight line = flat line = Single point = instantaneous speed speed A B faster speed constant speed no motion *

Who had a constant speed? A Describe B from 10-20 min. Graphing Motion Who started out faster? A (steeper slope) Who had a constant speed? A Describe B from 10-20 min. B stopped moving Find their average speeds. A = (2400m) ÷ (30min) A = 80 m/min B = (1200m) ÷ (30min) B = 40 m/min A B

Four steps to make a graph Step 1: Choose which will be the dependent and independent variables. The dependent variable goes on the y-axis and the independent variable goes on the x-axis.

Four steps to make a graph Step 2: Make a scale for each axis by counting boxes to fit your largest value. Count by multiples of 1, 2, 5, or 10. Scale must be consistent – if one line on the x-axis is equal to 1 hr the rest of the lines on the x-axis must be equal to 1 hr.

To determine scale, first you must determine the range of your data Step 2 Continued To determine scale, first you must determine the range of your data Range is equal to your highest data value Ex: If the range of your data is 0-23 your scale could be counting by 5s up to 25.

Four steps to make a graph Step 3: Plot each point by finding the x-value and drawing a line upward until you get to the right y-value.

Four steps to make a graph Step 4: Draw a smooth curve that shows the pattern of the points. Do not just connect the dots.

Data

Four steps to make a graph Step 1: Choose which will be the dependent and independent variables. The dependent variable goes on the y-axis and the independent variable goes on the x-axis. In the example which of the variables (time or distance) depends on the other? Dependent variable = Independent variable = Distance Time

Four steps to make a graph Step 2: Make a scale for each axis by counting boxes to fit your largest value. Count by multiples of 1, 2, 5, or 10. Scale for distance: 1 line = Range = Scale for time: 1 line = 10 km 60 1 hour 6

Distance (km) Time (hr) Step 3: Plot Points 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Distance (km) 1 2 3 4 5 6 Time (hr)

Step 4:Graph 0 10 20 30 40 50 60 Distance (km) 1 2 3 4 5 6 Time (hr)

get some graph paper from the metal tray on the front table get some graph paper from the metal tray on the front table. do the practice problems on your note sheet. Any not finished by the end of class are homework!

Wed. feb. 26 do now A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the helicopter’s acceleration? A skateboarder traveling at 9.0 m/s rolls to a stop at the top of a ramp in 3.0 seconds. What is the acceleration of the skateboarder? A race car accelerates from 18 m/s to 32 m/s in 2 seconds. Determine the acceleration of the car.

steeper slope = faster speed straight line = constant speed * 07/16/96 we have learned to analyze and make distance vs. time graphs. We saw that: A B slope = speed steeper slope = faster speed straight line = constant speed flat line = zero speed single point = instantaneous speed *

Now we will look at Speed vs. Time Graphs

Acceleration and Motion Graphs A speed vs. time graph is useful for showing how the speed of a moving object changes over time. If the line on the graph is horizontal, then the car is moving at a constant speed. There is no change in speed so there is no acceleration.

Slope You can use speed vs. time graphs to determine acceleration Remember: The “steepness” of a line is called its slope. Speed vs. Time

Slope -The slope is equal to the rise divided by the run -The slope for speed vs. time graph is therefore change in speed divided by time, which equals WHAT? ACCELERATION Slope = rise run Slope = change in v change in t Slope = 8-4 = 2 m s2 Speed vs. Time

Acceleration and Motion Graphs Positive acceleration adds more speed each second. Positive slope: the line slopes upwards

Acceleration and Motion Graphs Negative acceleration subtracts some speed each second, so things get slower. Negative slope: the line slopes downwards Speed is decreasing at the same rate.

Acceleration and Motion Graphs The position vs. time graph also shows acceleration. This graph is a curve when there is acceleration.

Review of terms: Distance: amount of space between 2 points Speed: how quickly something moves over a distance; distance divided by time Velocity: the same as speed but with a specific direction. Acceleration: the rate at which speed or velocity changes; change in speed divided by time

Reading Graphs: Position vs. Time x-axis (independent variable): Time y-axis (dependent variable): Position Slope = speed Horizontal line: at rest; speed is zero Straight line: constant speed; speed not changing positive slope = moving away from starting point negative slope = moving toward starting point Curved line: changing speed (acceleration) Speeding up or slowing down

Reading Graphs: Speed vs. Time x-axis (independent variable): time y-axis (dependent variable): speed Slope = Acceleration Horizontal line = constant speed; zero acceleration Straight line = constant acceleration (speed is changing at the same rate every second) positive slope = acceleration increasing negative slope = acceleration decreasing (deceleration)

Thur. Feb. 27 do now In the position vs. time graph what is graphed on the y-axis? On the x-axis? What is the independent variable? Dependent variable

Speed, Distance, and Time Quiz