More Practice: Distance, Speed, and Unit Conversion

More Practice: Distance, More Practice: Distance, Speed, and Unit Speed, and Unit

ConversionConversion

More Practice: Distance, More Practice: Distance, Speed, and Unit Speed, and Unit

ConversionConversion

More Practice: Distance, More Practice: Distance, Speed, and Unit Speed, and Unit

ConversionConversion

More Practice: Distance, More Practice: Distance, Speed, and Unit Speed, and Unit

ConversionConversion

More Practice: Distance, More Practice: Distance, Speed, and Unit Speed, and Unit

ConversionConversion

More Practice: Distance, More Practice: Distance, Speed, and Unit Speed, and Unit

ConversionConversion

More Practice: Distance, More Practice: Distance, Speed, and Unit Speed, and Unit

ConversionConversion

Vectors: Displacement Vectors: Displacement and Velocity: Learning and Velocity: Learning

GoalsGoals The student will be able to The student will be able to distinguish distinguish

between distance and displacement between distance and displacement and speed and velocity. (B2.1)and speed and velocity. (B2.1)

The student will be able to distinguish The student will be able to distinguish between between constant, instantaneous, and constant, instantaneous, and average speed and give examples of average speed and give examples of each involving uniform and non-each involving uniform and non-uniform motion uniform motion . (B3.1). (B3.1)

Vectors: Vectors: Displacement and Displacement and

VelocityVelocitySPH4CSPH4C

VectorsVectors

A vector quantity has both magnitude A vector quantity has both magnitude andand

VectorsVectors

A vector quantity has both magnitude A vector quantity has both magnitude and direction.and direction.

VectorsVectors

A vector quantity has both magnitude A vector quantity has both magnitude and direction.and direction.

The direction is given in square The direction is given in square brackets after the units:brackets after the units:

VectorsVectors

A vector quantity has both magnitude A vector quantity has both magnitude and direction.and direction.

The direction is given in square The direction is given in square brackets after the units:brackets after the units:

e.g., e.g., 5 km [West]5 km [West]

VectorsVectors

Examples of vectors:Examples of vectors: displacementdisplacement velocityvelocity

VectorsVectors

Examples of vectors:Examples of vectors: displacementdisplacement velocityvelocity accelerationacceleration

VectorsVectors

Examples of vectors:Examples of vectors: displacementdisplacement velocityvelocity accelerationacceleration forceforce etc.etc.

DisplacementDisplacement

Displacement is how far Displacement is how far an object is from its an object is from its starting position and is starting position and is notnot simply distance simply distance travelled + a direction.travelled + a direction.

d

DisplacementDisplacement

Displacement is how far an object Displacement is how far an object is from its starting position and is from its starting position and is is notnot simply distance travelled simply distance travelled + a direction.+ a direction.

E.g., the distance travelled here E.g., the distance travelled here by a driver commuting from by a driver commuting from Manhattan to N.J. was 14.5 km Manhattan to N.J. was 14.5 km even though the displacement even though the displacement was only 2.7 km [North].was only 2.7 km [North].

d

DisplacementDisplacement

ExampleExample: Ms. Rosebery walks 2 m : Ms. Rosebery walks 2 m [East] and then 1 m [West]. What [East] and then 1 m [West]. What was her distance travelled?was her distance travelled?

What was her displacement?What was her displacement?

DisplacementDisplacement

ExampleExample: Ms. Rosebery walks 2 m : Ms. Rosebery walks 2 m [East] and then 1 m [West]. What [East] and then 1 m [West]. What was her distance travelled?was her distance travelled?

What was her displacement?What was her displacement?

Distance travelled: Distance travelled: dd = 2 m + 1 m = = 2 m + 1 m = 3 m3 m

DisplacementDisplacement

ExampleExample: Ms. Rosebery walks 2 m : Ms. Rosebery walks 2 m [East] and then 1 m [West]. What [East] and then 1 m [West]. What was her distance travelled?was her distance travelled?

What was her displacement?What was her displacement?

Distance travelled: Distance travelled: dd = 2 m + 1 m = = 2 m + 1 m = 3 m3 m

Displacement: Displacement:

2 m

1 m

DisplacementDisplacement

ExampleExample: Ms. Rosebery walks 2 m [East] : Ms. Rosebery walks 2 m [East] and then 1 m [West]. What was her and then 1 m [West]. What was her distance travelled?distance travelled?

What was her displacement?What was her displacement?

Distance travelled: Distance travelled: dd = 2 m + 1 m = 3 m = 2 m + 1 m = 3 m

Displacement: Displacement:

She is She is 1 m [East]1 m [East] of her original starting of her original starting position.position.

2 m

1 m1 m

DisplacementDisplacement

We can represent [East] as the We can represent [East] as the positive direction and [West] as the positive direction and [West] as the negative direction:negative direction:

2 m

1 m1 m

DisplacementDisplacement

We can represent [East] as the We can represent [East] as the positive direction and [West] as the positive direction and [West] as the negative direction:negative direction:

= 2 m [East] + 1 m [West]= 2 m [East] + 1 m [West]

= + 2 m – 1 m= + 2 m – 1 m

2 m

1 m1 m

d

DisplacementDisplacement

We can represent [East] as the We can represent [East] as the positive direction and [West] as the positive direction and [West] as the negative direction:negative direction:

= 2 m [East] + 1 m [West]= 2 m [East] + 1 m [West]

= + 2 m – 1 m= + 2 m – 1 m

= + 1 m= + 1 m

2 m

1 m1 m

d

DisplacementDisplacement

We can represent [East] as the We can represent [East] as the positive direction and [West] as the positive direction and [West] as the negative direction:negative direction:

= 2 m [East] + 1 m [West]= 2 m [East] + 1 m [West]

= + 2 m – 1 m= + 2 m – 1 m

= + 1 m= + 1 m

= 1 m [East]= 1 m [East]

2 m

1 m1 m

d

DirectionsDirections

It is conventional to represent the It is conventional to represent the following directions as positive:following directions as positive:

forwardforward

DirectionsDirections

It is conventional to represent the It is conventional to represent the following directions as positive:following directions as positive:

forwardforward rightright

DirectionsDirections

It is conventional to represent the It is conventional to represent the following directions as positive:following directions as positive:

forwardforward rightright upup

DirectionsDirections

It is conventional to represent the It is conventional to represent the following directions as positive:following directions as positive:

forwardforward rightright upup NorthNorth EastEast

VelocityVelocity

Velocity is similarly Velocity is similarly notnot simply speed + simply speed + a direction.a direction.

VelocityVelocity

Velocity is similarly Velocity is similarly notnot simply speed + simply speed + a direction.a direction.

t

dvavg

VelocityVelocity

Velocity is similarly Velocity is similarly notnot simply speed + simply speed + a direction.a direction.

t

dvavg

time

ntdisplacemevelocityaverage

VelocityVelocity

ExampleExample: Ms. Rosebery walks 2 m : Ms. Rosebery walks 2 m [East] and then 1 m [West] in 3 s. [East] and then 1 m [West] in 3 s. What was her average speed?What was her average speed?

What was her average velocity?What was her average velocity?

VelocityVelocity

ExampleExample: Ms. Rosebery walks 2 m : Ms. Rosebery walks 2 m [East] and then 1 m [West] in 3 s. [East] and then 1 m [West] in 3 s. What was her average speed?What was her average speed?

What was her average velocity?What was her average velocity?

sm

avg s

m

t

dv 1

3

3

VelocityVelocity

ExampleExample: Ms. Rosebery walks 2 m : Ms. Rosebery walks 2 m [East] and then 1 m [West] in 3 s. [East] and then 1 m [West] in 3 s. What was her average speed?What was her average speed?

What was her average velocity?What was her average velocity?

sm

avg s

m

t

dv 1

3

3

][3.03

][1East

s

Eastm

t

dv s

mavg

Instantaneous VelocityInstantaneous Velocity

Average velocity is rarely calculated Average velocity is rarely calculated for an object changing direction. It for an object changing direction. It makes more sense to talk about themakes more sense to talk about the instantaneous velocityinstantaneous velocity, which , which isis the speed + the direction at that the speed + the direction at that particular instant.particular instant.

Instantaneous VelocityInstantaneous Velocity

Average velocity is rarely calculated Average velocity is rarely calculated for an object changing direction. It for an object changing direction. It makes more sense to talk about themakes more sense to talk about the instantaneous velocityinstantaneous velocity, which , which isis the speed + the direction at that the speed + the direction at that particular instant.particular instant.

Instantaneous VelocityInstantaneous Velocity

Assuming Ms. Rosebery walked at Assuming Ms. Rosebery walked at constant speed, what was her constant speed, what was her instantaneous velocity at:instantaneous velocity at:

1.5 s?1.5 s?

2 s?2 s?

2.5 s?2.5 s?

Instantaneous VelocityInstantaneous Velocity

Assuming Ms. Rosebery walked at Assuming Ms. Rosebery walked at constant speed, what was her constant speed, what was her instantaneous velocity at:instantaneous velocity at:

1.5 s?1.5 s? 1 m/s [East]1 m/s [East]

2 s?2 s?

2.5 s?2.5 s?

Instantaneous VelocityInstantaneous Velocity

Assuming Ms. Rosebery walked at Assuming Ms. Rosebery walked at constant speed, what was her constant speed, what was her instantaneous velocity at:instantaneous velocity at:

1.5 s?1.5 s? 1 m/s [East]1 m/s [East]

2 s?2 s? 0 m/s (while she is changing 0 m/s (while she is changing direction)direction)

2.5 s?2.5 s? 1 m/s [West]1 m/s [West]

Instantaneous VelocityInstantaneous Velocity

Assuming Ms. Rosebery walked at Assuming Ms. Rosebery walked at constant speed, what was her constant speed, what was her instantaneous velocity at:instantaneous velocity at:

1.5 s?1.5 s? 1 m/s [East]1 m/s [East]

2 s?2 s? 0 m/s (while she is changing 0 m/s (while she is changing direction)direction)

2.5 s?2.5 s?

More PracticeMore Practice

More Practice: Displacement and More Practice: Displacement and VelocityVelocity

and Graphing Motionand Graphing Motion