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Analyzing Displacement, Velocity and Vector Directions

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Presentation on theme: "Analyzing Displacement, Velocity and Vector Directions"— Presentation transcript:

1 Analyzing Displacement, Velocity and Vector Directions

2 Topics covered today Reviewing Scalar and Vector Quantities
New Terms: Displacement and Velocity How to identify Vector Directions The X-Axis Method The Navigator Method Example Problems Homework Assignment

3 Scalar and Vector Quantities
A scalar quantity is one that only indicates “how much” (the magnitude) of the quantity. Some examples are: Distance Speed Mass Time

4 Scalar and Vector Quantities
A vector quantity is one that indicates “how much” (the magnitude) AND the direction of the quantity you are interested in. Some examples are: Displacement Velocity Acceleration Force

5 Review Measured Quantity Scalar Vector 2.5m/s 55m/s 35o west of north
55m/s 35o west of north 350N downward 35km 40o east of north

6 What is Displacement? Displacement is a measurement of the change in distance and direction of an object from where it started from. It is also called change in position. Distance is the total length traveled, regardless of the direction that is traveled. Displacement is how far away you are from your starting (or reference) position and in what direction.

7 Finding Displacement To find the Displacement of an object, you simply need to: Choose a direction to treat as positive values. For example, if the object is moving right, then all movement to the right is positive and all movement to the left is negative. Add up your positive and negative numbers and you have your displacement.

8 Scalar and vector Example: Distance vs Displacement
Distance travelled is a scalar quantity. It is a measurement of the change in distance of an object moving from a starting reference point. d = 3 m + 5 m = 8 m Displacement is a vector quantity. It is a measurement of the change in distance and the direction or the change in position of an object from a reference point. d = 3 m [right] + −5 m [left] = −2 m [left]

9 An Example of Displacement
Distance = Displacement =

10 An Example of Displacement
Distance = Displacement =

11 What is Velocity? Velocity is a measurement of the change in displacement over time of an object. This is subtly different then speed, which is a measurement of the change in distance over time of an object. In most of the problems you’ll solve, the direction of motion doesn’t usually change so that the terms speed and velocity are interchangeable.

12 Finding Velocity The formula for finding Velocity is:

13 Practice A person walks 12.0 m [right] of a bus stop in 3.00 seconds. What is the average velocity? A car drives 2.5 km east at 18 m/s. How long does it take to reach their destination? A cyclist is training for a triathlon and rides her bike north at 5 m/s for 3.4 hours. What is her displacement?

14 Let’s compare Velocity to Speed
What’s the difference in the formula? Dan walked 12.0m from the bus stop, turned around and walked back 4.0m. Dan walked a total of 16.0m (non-directional). He accomplished this in 20.0s. Find Dan’s speed.  Dan walked 12.0m (E) from the bus stop, turned around and walked 4.0m (W). He accomplished this in 20.0s. Find Dan’s velocity.

15 Writing out scalars and vectors
Scalar quantities like speed and distance are written using the letters v and d without arrows above them. v is speed d is distance

16 Writing out scalars and vectors
Vector quantities like velocity and displacement are written using the letters and with arrows above them. is velocity is displacement

17 Identifying Vector Directions
The X – Axis Method This method uses the same grid as in Math 10. [up] and [right] are positive vectors. The x-axis is 0° and you measure the angle by going counterclockwise

18 Examples with X – Axis Method
Y Find the direction of the following vectors V1 = V2 = V3 = V4 = V5 = 9 m V1 50° V2 8 m X 40° 4 m 6 m 25° V5 V3 7 m V4

19 Examples with X – Axis Method
Y Find the direction of the following vectors V1 = V2 = V3 = V4 = V5 = 9 m V1 50° V2 8 m X 40° 4 m 6 m 25° V5 V3 7 m V4

20 Identifying Vector Directions
The Navigator Method This method uses the same grid as a compass. [N] and [E] are positive vectors. [North] is 0° and you measure the angle by going clockwise

21 Examples with Navigator Method
Find the direction of the following vectors V1 = V2 = V3 = V4 = V2 = 5m/s 30° V1 = 4m/s W E 20° V3 = 7m/s 15° V4 = 8m/s S

22 Examples with Navigator Method
Find the direction of the following vectors V1 = V2 = V3 = V4 = V2 = 5m/s 30° V1 = 4m/s W E 20° V3 = 7m/s 15° V4 = 8m/s S

23 Example Question #1 David moved 150 meters north in 40 seconds and then moved south 120 meters in 20 seconds? What is the distance he has traveled? What is the total displacement from his starting position?

24 Example Question #1 David moved 150 meters north in 40 seconds and then moved south 120 meters in 20 seconds? What is the distance he has traveled? What is the total displacement from his starting position?

25 Example Question #1 David moved 150 meters north in 40 seconds and then moved south 120 meters in 20 seconds? What is David’s overall average speed? What is David’s overall average velocity?

26 Example Question #2 Average distance and displacement?
Average speed and velocity?

27 Physics Assignment Practice Problems #6 – 10 (p139 - 141)
B.2.1 Check and Reflect (p145) Questions #3, #4

28 Before getting Started

29 Speed-time graphs Represent change in speed over time
Slope of line represents change of speed A speed vs. time graph plots time on the “x” axis and speed on the “y” axis. The slope of the speed vs time graph tells you if the object is speeding up or slowing down

30 Area Under a Speed vs Time Graph
The area under the best fit line of a speed vs. time graph can be calculated by finding the area Area = length x width = (v) x (∆t) = (m/s) x (s)

31 Practice: Speed-time graphs
A boat traveling along a shoreline passes people standing along the beach every two seconds. The people on the beach have a radar gun and record the speed of the boat as it passes. Time (s) Velocity (m/s) Calculate the slope of the line Calculate the area under the line.

32 Interpreting Speed – Time Graphs

33 Practice How do we calculate slope? What does slope mean?
What does a horizontal line mean? Uniform motion (staying the same) What does the area under the line represent? Distance How do we calculate this? Practice problem p 133 #5

34 Examples of DT and ST Graph Questions

35 Physics Assignment Practice: p135 #6, 13 ,18
B1.1: Check and Reflect (p135) Questions 4, 5, and 6, 12 and 13 are a review of the basics Questions 14 and 15 are detailed graphing questions that you need to know how to do successfully.

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