Do Now: ( 8 min) A man travels from New York to Los Angeles, a 3000 mile trip. He then travels to Las Vegas, which is 200 miles back towards New York. He takes a non-stop flight to LA which takes 5 hours. His flight to Vegas takes 1 hour. 1.What is his average speed? 2.What is his average velocity ?

Describing Motion Day 2

Displacement: The vector quantity defining distance and direction between two positions (How far something is from a starting position) Review Distance: A scalar quantity equal to the length of one or many displacement vector (How far something moves)

Objective: To apply what we know about scalar and vector quantities of motion to formulas about motion in order to prepare for a lab. To become familiar with the proper notation used to describe and explore motion.

Starting position: d i Final position: d f Displacement:  d = d f - d i

Time Interval

Time interval: (  t) time elapsed or taken

Average Speed

The ratio of the total distance traveled over the total time interval

Average Velocity (v)

The ratio of the total displacement over the total time interval

v =  d/  t v = d f - d i  t f - t i

Instantaneous Velocity

Instantaneous velocity:the speed & direction at a particular instant

Example #1: Time Interval A car begins traveling to New York at 3:00 and arrives at 6:30. What was the time it took to travel? 6:30-3:00 = 3.5 h

Example #2: Average Speed A car starts traveling North to New York which is 200 miles away in 4 hours. What was its average speed? 200/4 = 50 mph

Example #3: Average Velocity A car traveled 200 mi North from Baltimore to New York in 4 hours. What was its average velocity? 200mi/4 h = 50 mph North

Example #4: Instantaneous Velocity A car begins traveling North at 3:00 at 60 mph. It speeds up by 10 mph at 4:00. What was its instantaneous velocity at 4:00? = 70 mph North at 4:00

Acceleration

Acceleration: The change in velocity per unit time Units: v/t = (m/s)/s = m/(s X s) = m/s 2 (unless otherwise stated in the problem)

Average Acceleration

a =  v/  t a = v f - v i  t f - t i

Example #5 A car goes from, 0 – 60 m/s in 5 s. What is its acceleration? (60m/s-0m/s)/5s = 12 m/s 2

Example #6 An airplane takes off from rest and reaches a speed of 400 m/s in 10 s. What is its acceleration? (400m/s-0m/s)/10s = 40 m/s^2

Practice Begin working on your homework. It is due Wednesday September 28

Do Now (9/27): (4 min) A NASA rocket blasts off from 0 m/s to 500 m/s in 12 s. What is its acceleration?

Reminders: When solving problems, you must show all work for credit!!! This means: Listing variables: d= 3m, t=4s, s=? showing a formula: s=d/t plugging in: s = 3m/4s boxing your answer with the correct notation and units S =.75 m/s

When solving word problems, look for context clues to tell you what you’re solving for Distance ( measured in m): How far something went How high/large/small something is Where something is or moved to Time (measured in s): How long it took How much time passed Velocity/speed: (measured in m/s) The rate of an object How fast something traveled Acceleration (measured in m/s 2 ): How fast something sped up How fast something slowed down

Mini Quiz: If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s 2 for 3 seconds, what will its final velocity be?

Do Now (9/28): If a car accelerates to a velocity of 60 m/s, at a rate of 50 m/s 2 for 4 seconds, what was its initial velocity?

Objective: To use what we know about displacement, time velocity, and acceleration to graph different types of motion To practice making graphs to prepare for a lab on motion

Distance/Position vs. Time Graphs

Example: You went for a walk to the near by store (10 km north) and back to your original reference point. This would mean your total travelled distance is 20 km (10km to the store, and 10km back). This distance-time graph would look like the following: What’s the difference? Discuss!

Position-time graphs Position graphs depend on direction (remember displacement, which is the change in position, is a vector quantity)

Graphing Position-Time Graphs Time is always the I.V. (x-axis) Position is always the D.V. (y-axis) Is this graph linear?

Example: Time (t) measured in sPosition (x) measured in cm ∆x= change in position (aka displacement); displacement can be represented by any variable that represents position (x, y, d, etc.) ∆t= change in time

Finding the average velocity Draw a line of best fit and find the slope What is the slope of this line?

Practice: Directions: 1.Work with a partner. Have one partner get a whiteboard and dry erase marker. 2.Create the graph on the board in the time provided. 3.Draw a line of best fit and find the velocity (slope). 4.Present your graph when finished. Example #1: Time (t) measured in sPosition (x) measured in m

Practice: Example #2: Time (t) measured in sPosition (x) measured in m Directions: 1.Work with a partner. Have one partner get a whiteboard and dry erase marker. 2.Create the graph on the board in the time provided. 3.Draw a line of best fit and find the velocity (slope). 4.Present your graph when finished.

Graphing Data

1 st Order: y = 2x

2 nd Order Curve Y = x 2

3 rd Order Curve y = x 3

Velocity/Time Graphs v/t graphs are identical to p/t graphs except that velocity is graphed on the y-axis instead of position. The slope of a v/t graph is… acceleration!

Practice: Directions: 1.Work with a partner. Have one partner get a whiteboard and dry erase marker. 2.Create the graph on the board in the time provided. 3.Draw a line of best fit and find the velocity (slope). 4.Present your graph when finished

Examples of position-time and velocity-time graphs

Constant Speed p/t graph The motion is linear Rate of change is constant – the position increases by the same amount for every time interval This means the slope (which represents the velocity) is constant

Changing Speed p/t graph The motion is non-linear Rate of change is changing– the position increases by a different amount for every time interval This means the slope (which represents the velocity) is changing Changing velocity means… acceleration!

Examples: Constant Velocity Positive Velocity Positive Velocity Changing Velocity (acceleration)

Constant acceleration v/t graph For a v/t graph, slope represents acceleration – constant slope means constant acceleration

But what if there’s no acceleration?

For no acceleration, use the following graph: Positive Velocity Zero Acceleration

Motion Lab Graphs Use the remainder of the period to work on your graphs Remember, you need an IDEAL graph for each of your eight graphs, as well as the graphs of your data. Use the graphs we just went over to create your ideal p/t and v/t graphs for constant speed and changing speed (acceleration) – you should have four graphs of each

Do Now (9/29) Describe the motion of each graph:

Do Now (9/29) Describe the motion of each graph: