Scalar & Vector QuantitiesDistance vs Displacement (today)

Speed vs Velocity

Fastest & Furthest

Scalars

There are two ways to describe motion:

using scalars and using vectors

Scalar Quantities: have magnitude, but

not direction

“how fast”

“how far”

Scalars do not tell us what direction

Magnitude = “how much”

Scalars

ex) Calgary is approximately 200 km away from

Lethbridge

This is a statement of scalar quantity. It tells us how

far (200 km) but not the direction

ex) ________________, the cheetah, ran at 110 km/h.

This is also a scalar statement. It tells how fast, but

not the direction the cheetah ran.

Some Typical Scalars

Distance – How far an object has moved (Symbol: d)

Speed – How far an object has moved in a period of

time (symbol: v)

Time – (Symbol: t)

Vectors

Vector quantities have both magnitude and

direction.

ex) Calgary is 200 km North of Lethbridge

ex) “Boys at 230 m South.”

– Koreen’s husband

These are vector statements.

Some Typical Vectors

Displacement – measures the change in distance

and change in direction; the change in position of

an object. Symbol: 𝒅

Velocity – speed and direction of an object; the

rate of change of an object’s position. Symbol: 𝒗

The little arrow on top of the symbols is called a vector

arrow. It is used to distinguish between distance/

displacement and speed/velocity.

Example 1

1. You walk 275 m West towards school, and then

realize you forgot your super important

science homework at your friend’s house, so

you turn around and walk 424 m East to get

the homework.

a) What is your distance traveled?

b) What is your displacement?

Example 2

1. A cat walks 450 cm West and then turns around and

walks 212 cm East. What is the cat’s displacement?

Strategy 1:

Strategy 2:

Example 3

When your chickens go on strike and start marching around

the yard. They march 27.7 m [S] and then turn around and

march 21.4 m [N].

a) What distance (∆d) do the chickens travel?

a) What is the chickens’ displacement ( )?

• Strategy 1:

• Strategy 2:

? When would distance and displacement have the

same magnitude?

Displacement vs Distance

Answers to practice

problems

1)a) 700m b) 150 m [W]

2)a) 680 m b) 0

3)a) 12 m b) 0

4)a) 5.00 m [N] b) 1.56 m/s