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Motion and Energy Chapter 9 Section 1 and 2. By Mrs Nazarali. Vector & Scalar Quantity. A vector quantity is a quantity that has both magnitude and direction. A scalar quantity is a quantity that has magnitude, but no direction. Which is a vector and which one is scalar ?.

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vector scalar quantity
Vector & Scalar Quantity
  • A vector quantity is a quantity that has both magnitude and direction.
  • A scalar quantity is a quantity that has magnitude, but no direction.
which is a vector and which one is scalar
Which is a vector and which one is scalar ?
  • Velocity – 55 miles/hr driving east
  • Speed -55 miles/hr
  • Weight (gravitation pull)
  • Mass
  • Time
  • Volume
  • Force
extracting key points questions
Extracting Key PointsQuestions:
  • 1. When do we say that a body is in motion?
  • 2. When do we say that an object moves faster than another object?
so where are you
So, where are you?

Where you will meet is the position as described by a reference point. A reference point is an object that does not move.

You and your friend agreed to meet for a movie tonight. You decided to get together at the corner of Orange and Denni. in 30 minutes.

Click the object for a history of clocks

it s about time
It’s about time!

The time you will meet is measured with a clock. Time is defined as the interval between two events (when you make the decision to meet and when youmeet).

Over the years, time has been measured with sundials, hour glasses, watches, and the most accurate clock, the atomic clock.

slide7

As you walk to meet your friend, you change your position with every step you take. Distance is how far you travel along a path while you change your position.

SI

Distance is measured in

units.

SI stands for the International System of Units called the metric system, a system based on the number ten. The basic unit of length is the meter (m).

Do you want to know more about units of length and the metric system?

Visit these links

Metric System

SI

Metric Numbers

How Many?

slide8

While you were walking to meet your friend, you were in motion. Changing position creates motion.

You have gone a distance, and time has passed while you were changing your position.

let s talk displacement
Let’s talk displacement-

Displacementis the change in position of an object. If you end up where you started, your displacement is zero.

Displacement is described by both a length and a direction.Distance is described only by length. To say that you live 6 km from the amusement park isn’t very helpful unless you state in which direction (6 km south).

distance vs displacement
Distance vs. Displacement

Vector – msmt with a size and direction

Distance

Total length of a path b/w two points.

Displacement

Length and direction of a straight line b/w starting and ending point.

slide12

The better way to describe the difference between displacement and distance is here:1. Displacement is the directed line segment between initial and final position of a moving body.2. Distance is the total length of path traversed by the moving body irrespective of direction.

o k just how fast are you moving
O.K. Just how fast are you moving?

Speedis the distance traveled by an object during a given time interval (distance divided by time) .

=

Distance

Speed =

Time

Speed = distance travelled per unit of time

SI unit: m s

average speed
Average speed

A car travels at 50 km h–1,

slows down to 0 km h–1,

and speeds up again to 60 km h–1.

Its average speed over the whole journey

overall distance travelled

=

total time of travel

velocity
Velocity

When you know the speed and direction of an object’s motion, you know the velocity of the object.

The wind is out of the southwest at 10 km/hr.

For example, the meteorologist (one who studies the weather) gives the velocity of the wind.

Velocity is the displacement of an object divided by time.

slide16

The formula for velocity is-

Displacement

Velocity =

Time

=

In the formula, v stands for average velocity and dfor displacement. Time is t.

d

v =

t

these are your equations
These are your equations

Distance

Speed =

Time

Displacement

Velocity =

Time

speed with direction

Velocity

Speed with direction

speed = 90 km h–1

Pilots are concerned about velocity (direction & speed).

speed = 300 km h–1

direction = west

graphing motion
Graphing Motion
  • Slope = rise = distance = speed

run time

  • Graph distance on the y-axis and time on the x-axis
learning checkpoint
Learning Checkpoint
  • This graph shows several stages of motion:
    • Stage 1: 100 m in 10 s
    • Stage 2: 50 m in 10 s
    • Stage 3: 150 m in 20 s
  • Calculate the speed as indicated by each of the colors.
  • Calculate the average speed.
  • What is the total distance?
solution
Solution

Stage 1: S= d/ t

100 m/ 10 s= 10 m/s

Stage 2: S= d/t

50 m/ 10 s= 5 m/s

Stage 3: S= d/t

150 m/ 20 s= 7.5 m/s

Ave Speed= Tot d/ Tot t

300 m/ 40 s= 7.5 m/s

Distance = 300 meters

slide24

A cheetah can maintain a constant speed for short periods of time. Its speed is the same at all times during its motion. In 4 minutes, the cheetah traveled 8 km.

8 km

speed =

= 2 km/min

4 min

Most objects do not move at constant speeds for very long. Dividing the total distance by the total time does not tell you the speed for every point of the journey. Instead it gives you the average speed.

The rabbit had a burst of speed during the second minute. What is going on between the 3rd and 4th minutes?

Distance

10 8 6 4 2

0 1 2 3 4

Time

The rabbit is not moving. Time passes but no distance is covered.

Distance

Answer

total distance

0 1 2 3 4

average speed =

Time

time interval

slide25

Let’s manipulate that formula-

Suppose you were given the speed and the time. Could you determine the distance?

v = 2 km/min t = 4 min

d = 8 km

Yes. d = v t

This time you know the distance and the speed. Can you find out how long it took for the cheetah to go the distance?

Yes. t = d / v

slide26

Instantaneous speed-

Instantaneous speed is the rate of motion at any given instant. What does that mean?

The picture at the right gives you the speed of the runner at the instant the picture was taken.

8.5 meters/second

6

767

76

6

slide27

The speedometer in your car gives you a reading of instantaneous speed.

8.5 meters/second

6

767

76

While the speedometer is showing the speed at any given moment

005

6

6

slide29

The speed of a ship is 50 km/hr. How far will it travel in 10 hours? (Something different here!)

500 km

Distance = speed x time

Check for your answer 

A friend lives 4 km away. Walking at 2 km/hr, how long will it take you to go this distance? (Be careful---it’s another version of the formula!)

2 hrs

time = distance/speed

Check for your answer 

slide30

Let’s work a problem or two-

An airplane is flying from Bridgeport, WV, to Washington, DC., a distance of 330 km. The trip takes 1.5 hours. What is the airplane’s velocity?

The total displacement divided by total time is a velocity of 220 km/hr east.

Click here for the answer.

A girl walks 2 km west, she turns and walks 3 km east. What distance does she walk? What is her displacement?

The distance she walked 5 km. Her displacement is 1 km east.

Click here for the answer.

problems
Problems

Car trip: 100 km first 2hr

150 km next 3hr

Avg Speed = total distance

total time

= 100 + 150

2 + 3

= 250

5

= 50km/hr

Car trip: 80km/hr for first hr

40km/hr next 2hr

Avg Speed = total distance

total time

First hr = 80km

Next 2hr = 80km

= 80 + 80

2 + 1

= 160

3

= 53km/hr