Motion Chapter 9

Describing & Measuring Motion ALCOS 8: Identify Newton’s 3 Laws of Motion Objectives: Determine when an object is in motion

What is Motion? Motion is when the distance from one object to another is changing. We can use a reference point for comparison to determine if something is in motion. Tree, building, etc. An object is in motion if it changes position relative to the reference point. Why wouldn’t we want to have a reference point that moves?

Relative Motion This is when an object’s motion depends on the reference point. Are you moving if the reference point is your desk? No- the distance between you and your desk does not change.

Relative Motion Are you moving if the reference point is the sun? Yes- the sun is constantly moving, therefore, the distance between you and the sun is constantly changing!

Distance The amount of space between two objects When you measure distance, you measure length. SI Unit for length: Meter (m) Remember: SI units are the system used by scientists throughout the world. We don’t use inches, feet, yards, etc.

How many jumps does it take? Ladder Method 1 2 3 KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit Meters Liters Grams CENTI 0.01 Unit MILLI 0.001 Unit How do you use the “ladder” method? 1st – Determine your starting point. 2nd – Count the “jumps” to your ending point. 3rd – Move the decimal the same number of jumps in the same direction. 4 km = _________ m Starting Point Ending Point How many jumps does it take? 4. 1 __. 2 __. 3 __. = 4000 m

9.1 Describing & Measuring Motion Review True/False An object is in motion if the distance between the object and a reference point stays the same. False. An object is in motion when the distance between the object and the reference point changes.

9.1 Describing & Measuring Motion Review Which of the following is NOT a good example of a reference point? Wall Tree Car Building Car. The car is not a good reference point because it can move and would make measuring distance difficult.

9.1 Describing & Measuring Motion Review What is the SI unit for distance? Liter Meter Gram Mile Meter. We may use conversions of the meter (kilometer, centimeter, etc., but will only use the metric system)

Objectives: Be able to 9.2 Speed & Velocity Define speed, average speed, velocity and instantaneous speed. Calculate speed Graph motion

Speed The distance an object travels per unit of time Can be calculated using the formula: Speed = Distance ÷ Time Unit = Meters/Second

Calculating Speed Example: A dog travels 5 meters in 5 seconds. What is the dog’s speed? Speed= Distance÷ Time Speed= 5 meters ÷ 5 seconds Speed= 1 meter/second

Using the Speed formula to Calculate Distance Example: A car travels at a speed of 50 km/hour for 4 hours. How far has the car traveled? Speed = Distance ÷ Time Plug in what you know 50 km/hour= Distance / 4 hours We want to get distance by itself so multiply both sides by the time. 4 hours x 50 km/hour = Distance 200 km= Distance– Hours cancel out!

Using the Speed Formula to Calculate Time Example: How long does it take a person jogging 2 m/s to travel 1000 meters? Speed = Distance ÷ Time Plug in what you know 2 m/s = 1000 m / Time We need to get time by itself so multiply both sides by time: Time x 2 m/s = 1000m (time cancels out on the right side) Time= 1000m/2m/s (meters cancel out) Time = 500 seconds (a little over 6 minutes)

Average Speed The overall rate of speed at which at object moves. Formula: Average Speed = Total Distance ÷ Total Time Unit= Meters/Second

Calculating Average Speed Example: A student walks from Mrs. Casey’s class to Mrs. Walton’s class between 3rd and 4th periods. In the first 45 seconds, the student travels 15 meters. In the next 15 seconds they travel 2 meters. In the last 30 seconds they travel 13 meters to Mrs. Walton’s door. What is their average speed?

Calculating Average Speed Formula: Average speed = Total Distance ÷ Total Time Make a T chart with 2 columns labeled distance and time. Add up the total distance traveled and the total time Total Distance = 30 meters Total Time = 90 seconds Average Speed = Total Distance ÷ Total Time Average Speed = 30 meters ÷ 90 seconds Average Speed = 1 meter/3 seconds

DSW 1-6 You ride your bike for 25 minutes at a rate of 0.5 km/minute. How far have you traveled? A train travels 225 km in 2.5 hours. What is the train’s speed? How long would it take you to swim across a lake that is 900 meters across if you swim at a rate of 1.5 meters/second?

#1 You ride your bike for 25 minutes at a rate of 0.5 km/minute. How far have you traveled? 12.5 m 50 m 50 km 12.5 km Speed=Distance/Time 0.5 km/min= Distance/25 min 25 min x 0.5 km/min = Distance 12.5 km = Distance

#2 A train travels 225 km in 2.5 hours. What is the train’s speed? 90 km/hr 90 hr 562.5 hr Speed= Distance/Time Speed=225 km/2.5 hr Speed= 90 km/hr

#3 How long would it take you to swim across a lake that is 900 meters across if you swim at a rate of 1.5 meters/second? 600s 600m/s 1350m 1350s Speed= Distance/Time 1.5m/s= 900m/Time Time=Distance/Speed Time=900m/1.5 m/s Time=600s

Velocity Speed in a given direction Example: A bird flies 20 km/hour South You must have speed AND direction to have velocity

Instantaneous Speed The rate at which an object is moving at a given instant in time. We can find this using a distance versus time graph. To find instantaneous speed, find the slope of the line that goes through that point in time.

Instantaneous Speed Example: Looking at the graph we just drew, what was the instantaneous speed at 6 seconds? Find time-6 seconds on the graph. Find the slope of the line that goes through that point. Slope= Rise/Run Slope=3/3 Slope=1 Speed=Slope Speed= 1 m/s Example: What was the instantaneous speed at 10 seconds? Find time 10 seconds on the graph. Flat line= no slope Slope 0=Speed 0 m/s

DSW 1-10 No Clickers Today! Draw a graph that shows an object traveling at a rate of 10 m/s for 10 seconds. How far has the object traveled after 4 seconds in the graph below? What is the average speed for the entire trip?

The rate at which velocity changes Acceleration The rate at which velocity changes Remember velocity= speed & direction This means that acceleration must be a change in speed or a change in direction

Ways to Accelerate Increase Speed Decrease Speed Change direction Called acceleration A car starts to move when the light turns green. Decrease Speed Called deceleration or negative acceleration A car slows to a stop at a red light Change direction An object traveling at a constant speed that is changing direction has acceleration A person riding on a merry-go-round accelerates as the ride spins.

Calculating Acceleration A change in speed per unit of time Acceleration= (final speed-initial speed)/time Units= m/s2

Calculating Acceleration Example: A car at a red light accelerates to 30 m/s over a 5 second time period. What is the acceleration? Acceleration= (final speed-initial speed)/time Acceleration= (30 m/s – 0 m/s)/5 seconds Acceleration= (30 m/s)/5s Acceleration= 6m/s2

Calculating Acceleration A soccer ball moving at a rate of 8 m/s slows to a stop over a 4 second time period. What is the acceleration? Acceleration= (final speed-initial speed)/time Acceleration= (0 m/s – 8 m/s)/4 seconds Acceleration= (-8 m/s)/4s Acceleration= -2m/s2

DSW 1-11-12 Get your clicker! A car is traveling at a rate of 25 m/s and increases their speed to 40 m/s over a 5 second time period. What is the car’s acceleration? A hockey puck moving at a speed of 10 m/s slows to a stop over a 10 second time period. What is the hockey puck’s acceleration?

DSW #1 A car is traveling at a rate of 25 m/s and increases their speed to 40 m/s over a 5 second time period. What is the car’s acceleration? 3 m/s 3m/s2 5 m/s -5 m/s2 A= (f-i)/time A=(40 m/s – 25 m/s)/ 5s A= (15 m/s) / 5s A= 3 m/s2

DSW #2 A hockey puck moving at a speed of 10 m/s slows to a stop over a 10 second time period. What is the hockey puck’s acceleration? 1 m/s 10 m/s2 10 m/s -1 m/s2 A= (f-i)/time A=(0 m/s – 10 m/s)/ 10s A= (-10 m/s) / 10s A= -1 m/s2

Motion & Graphs Motion graphs are an important tool used to show the relationships between position, speed, and time. It’s an easy way to see how speed or position changes over time These types of graphs are called kinematic graphs. There are two types: Position vs. Time graphs Speed vs. Time Graphs

Position Vs. Time Used to show an object’s position at a given time. Position: on y-axis Time: on x-axis

Creating a Distance vs. Time Graph Draw the x and y axis and label them with the correct units. X is always time and Y is always distance Plot points on the graph from the data table. Connect each dot with a straight line.

You Try It: Graphing Position Vs. Time Suppose you are helping a friend who is training for a track meet. She wants to know if she is running at constant speed. You mark the track in 50-meter increments and measure her time at each position during a practice run. Create a position-time graph using her data. Time (s) Position (m) 10 50 20 100 30 150

You Try It: Graphing Position Vs. Time What would her speed be? 50m/10s = 5 m/s 100m/20s = 5 m/s Notice that this is a straight line - why?? She is moving at a constant speed - neither slowing down nor accelerating

You Try It: Graphing Position Vs. Time #2 Graph the motion of this car. Graph the points: (0,0), (1, 10), (2, 20), (3, 30), (4, 40), (5, 50). Your graph should look like this…

What does slope have to do with it? Slope is the ratio of the rise (y-axis) to the run (x-axis) of a line on a graph. A bigger slope means a steeper line which means a faster speed.

Steeper Line = Faster Speed

Negative Slopes What does this graph mean??? And this one? They show an object that is slowing down - or decelerating. The first graph is slowly decelerating, while the second graph is quickly decelerating.

This is another really good graph to draw in your motion math little book

Graphing Practice Create a graph for a person that walks at a rate of 1 meter per second for 5 seconds. Steps: First we will need to make a data table that shows the distance traveled and the time it took. Find the distance traveled after each second. Now make your graph and plot the points. Make sure to label your axis!

Graphing Longer Trips Create a distance vs. time graph for the following data: Distance (m) Time (s) 8 0-4 3 5-8 8-11 4 12-15