Vectors: Vectors: Displacement and Displacement and

VelocityVelocity

VectorsVectors

Examples of vectors:Examples of vectors: displacementdisplacement velocityvelocity accelerationacceleration

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 rightright upup NorthNorth EastEast

VelocityVelocity

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

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?

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?

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.

10m due North + 7m due 10m due North + 7m due SouthSouth

15km due East + 20km due 15km due East + 20km due West + 55km due EastWest + 55km due East