Motion Unit

Grade 10 Science

Chapter 11

Displacement and Acceleration

Introductory Activity 

From Here to There (Use GPS Compass and Paces) Giving directions isn’t always easy – it forces us to think about things we do automatically. (a)    Working in a group, write clear instructions from where you are to some other location in your school.(b)   Produce a map, drawn to scale, showing the route to the target location(c)    Exchange instructions and/or maps with another group and try to reach their target location by following their directions(d)   Evaluate the other group’s map and instructions. Suggest a better form of communication? Suggest some improvements to the instructions. What are some sources of uncertainty? How confident are you in their set of instructions?

GPS Activity

• Using the GPS’s and longitude and latitude, create a scavenger hunt

• Choose a word with 6-8 letters and place 1 letter from the word at each of the points on your map

• Unscramble the word when you complete the scavenger hunt.

11.1 Vectors : Position and Displacement Question : If you leave home on a trip, and then end up back at home at the end of the trip, the total distance travelled is not zero, but something is zero. What is zero, and , how does this depend on direction?    Question : How can we show direction on a graph?    Question : When providing directions for a visitor, what are some of the different ways to indicate direction?

 

All distances and directions are generally stated relative to some reference point, which is usually the origin or starting point. For example if you go on a trip most people would say their reference point or origin is their home. Your position is the separation and direction from a reference point. For example you may be at a position of 152 m [W] – one hundred and fifty two meters west of the reference point.  

 152 m [W] 0  

 

A change in position ( d ) is known as displacement. means “the change in” and

d means “ change in position”.

d = d 2 - d 1 A change in position from one point to another is calculated using the above formula.

d = d 2 - d 1

d = (152 m) - (0)

d = 152 m [W]

Symbol Format 

When communicating a vector quantity, the value is accompanied by a direction

Direction is best communicated with a direction from a compass needle not forwards or backwards

Example : d = 38 km [W]

 

Drawing Vectors 

An alternative way of communicating a vector quantity is to draw a vector. A vector is a line segment that represents the size and direction of a vector quantity. Example : 

1 cm = 25 km

A quantity that involves a direction, such as position, is called a vector quantity.A vector quantity has both size (152m) and direction [W]. A quantity that involves only a size, such as distance, (250 km) is called a scalar quantity.

A scalar quantity has no direction.

 

Assignment:Q1-8 pg 417CBL Velocity Lab #1

11.3 Adding Vectors Along a Straight Line Two vectors can be added together to determine the result (or resultant displacement). Vector Diagrams

When you add vector quantities such as displacementyou need to consider both the size and direction of each quantity being added.

Use the “head to tail” ruleJoin each vector by connecting the “head” and of a vector to the“tail” end of the next vector

d1 d2

dR Resultant vector

Anne takes her dog, Zak, for a walk. They walk 250 m [W] and then back 215 m [E] before stopping to talk to a neighbor. Draw a vector diagram to find their resultant displacement at this point.

Scale Diagram Method

Vector Scale Diagram Method1)State the direction (e.g. with a compass symbol)

2)List the givens and indicate the variable being solved

3)State the scale to be used 4)Draw one of the initial vectors to scale

5)Join the second and additional vectors head to tail and to scale

6)Draw and label the resultant vector

7)Measure the resultant vector and convert the length using your scale 8)Write a statement including both size and direction of the resultant vector

0.70 cm x 50m / 1 cm = 35m [W]

d1 = 250m [W], d2 = 215m [E], dR = ?

1 cm = 50 m

dR

The resultant displacement for Anne and ZackIs 35 m [W].

Adding Vectors Algebraically

This time Anne’s brother, Carl, takes Zak for a walkThey leave home and walk 250 m [W] and then back 175 m [E] before stopping to talk to a friend. What is the resultant displacement at this position.

Adding Vectors AlgebraicallyWhen you add vectors, assign + or – direction to the valueof the quantity.

(+) will be the initial direction(-) will be the reverse direction

1.Indicate which direction is + or –

2.List the givens and indicate which variable is being solved

 

250 m [W] will be positive

d1 = 250 m [W], d2 = 175 m [E], dR = ?

3.Write the equation for adding vectors   

4.Substitute numbers(with correct signs) into the equation and solve

5.Write a statement with your answer ( include size and direction)

d1 + d2dR =

dR = (+ 250 m) + (-175 m)dR = + 75 m or 75 m[W]

The resultant displacement for Carl and Zak is 75 m[W]

Combined MethodZak decides to take himself for a walk.

He heads 30 m [W] stops, then goes a farther 50 m [W] before returning 60 m[E].

What is Zak’s resultant displacement?

Combined Method for representing vectors 1)State which direction is positive and which is negative

2)Sketch a labeled vector diagram – not to scale but using relative sizes

West is positive, East is negative

30m50m

60m dR

3)Write the equation for adding the vectors

4)Substitute numbers( with correct signs) into the equation and solve

5)Write a statement with your answer (including size and direction)

dR = d1 +d2 +d3

dR = (+ 30 m) + (+50m) + (-60m) dR = + 20m or 20m [W]

The resultant displacement for zak is 20 m [W]

Assignment

• Questions 1-7 pg 423

11.7 Describing Motion in Words This lesson introduces you to the terms associated with kinematics, the study of motion. The key ideas are position, distance, and displacement which were all studied in previous lessons. The new terms are speed and velocity, which are closely related. Velocity is a vector: it is just speed with direction.  Speed is a scalar: it is just speed

Objects with constant velocity have uniform motion. Velocity:the distance traveled by a moving object per unit of time.

 11.7 Describing Motion in Words A speed along with a direction is a vector, which means that the direction and the size (speed) stay the same. 

On a plane trip from Toronto to Winnipeg the pilot will usually announce an air speed such as 425 km/h. However, both the pilot and passengers know that the direction is west, so the velocity is 425 km/h [W]

Average velocity 

Average velocity is defined as the rate of change in position from start to finish. It is calculated by dividing the resultant displacement ( which is the change in position ) by the change in time.  

Vav = d R t

Comparing average speed with average velocity

Average Speed Average Velocity

Velocity only gives distance and time.

d

V t

Kilometers (km) orMeters (m)

Hours (h) orSeconds (s)

Speed/Velocity (km/h) or(m/s)

From Chapter 10

From Chapter 10

Average Velocity: the speed of moving objects is not always constant: 

Average Velocity = total distance / total time

Vav

d tot

t tot

d tot= d2 – d1

t tot= t2 – t1

Since speed is distance/time, we can write:  Speed = distance (10m) = 5 m/s  time (2s)No direction but …

Velocity is… speed in a given direction. e.g. Sydney walks 3 kilometers north for 2 hours .This is because…  Velocity = Displacement 3km[N] = 1.5 m/s[N]

Time(2h)Velocity must have the same units as speed -normally in physics we use m/s or km/h.

Velocity includes both d = change in displacement with a direction

t = change in time

V t

dA B

0m 5m

5s

N5m[E] / 5s = 1m/s [E]

 Average Velocity is… change in resultant displacement (dR) change in time(t)

Vav

dR

t

5m resultant

A

B C

3m

4m

1s

1s

5m [SE] / 2s = 2.5 m/s [SE]

Leon walks quickly around the outside of a basketball court. She walks 50 m north, 25 m east and 50 m south. This takes 50 seconds.

1.What is the distance she has walked?

2.What is her final displacement?

3.What is her velocity?

4.What is her average velocity?

Work these out, then check your answers

50m

25m

50m

dR

(50+25+50)m =125m

50m[N] + 25m [E] + 50m[S] = 25m[E]

125m / 50 s = 2.5m/s

25m[E] / 50s = 5m/s [E]

Assignment

• Questions 1-7 pg 436