1.1
Distance, Displacement
Distance

Distance (d) – how far an object travels.


Imagine an ant crawling along a ruler.
0
cm

Does not depend on direction.
1
2
3
4
5
6
7
8
What distance did the ant travel?

d = 3 cm
9
10
Distance
Distance does not depend on direction.
 Here’s our intrepid ant explorer again.

0
cm

1
3
4
5
6
7
8
9
Now what distance did the ant travel?


2
d = 3 cm
Does his direction change the answer?
10
Distance


0
cm


Distance does not depend on direction.
Let’s follow the ant again.
1
2
3
4
5
6
7
8
9
What distance did the ant walk this time?
d = 7 cm
10
Displacement

Displacement (d) – difference between an object’s
final position and its starting position.





Does depend on direction.
Displacement = final position – initial position
d = dfinal – dinitial
In order to define displacement, we need directions.
Examples of directions:



+ and –
N, S, E, W
Angles
Displacement vs. Distance

Example of distance:


Example of displacement:


The ant walked 3 cm.
The ant walked 3 cm EAST.
An object’s distance traveled and its
displacement aren’t always the same!
Displacement

Let’s revisit our ant, and this time we’ll find
his displacement.
- +
0
cm
1
2
3
4
5
6
7
8
Distance: 3 cm
 Displacement: +3 cm


The positive gives the ant a direction!
9
10
Displacement

Find the ant’s displacement again.

Remember, displacement has direction!
- +
0
cm
1
2
3
4
5
Distance: 3 cm
 Displacement: -3 cm

6
7
8
9
10
Displacement

Find the distance and displacement of the
ant.
- +
0
cm
1
2
3
4
5
Distance: 7 cm
 Displacement: +3 cm

6
7
8
9
10
Displacement vs. Distance

An athlete runs around a track that is 100 meters
long three times, then stops.

What is the athlete’s distance and displacement?



Distance = 300 m
Displacement = 0 m
Why?
Vector vs Scalar

Most of the
quantities used to
describe motion
can be categorized
as either vectors
or scalars.

A vector is
described by
magnitude (size)
and direction

A scalar is
described by
magnitude (size)
only
Review




A quantity that is
ignorant of direction is
referred to as a
_________________.
a. scalar quantity b.
vector quantity
3. A quantity that is
conscious of direction
is referred to as a
_________________.
a. scalar quantity b.
vector quantity

a. scalar quantity

B. vector quantity
Distance vs- Displacement
I. Distance and Displacement
1) Distance and displacement are similar
but different
a) Distance is a scalar quantity which
refers to “the amount of ground an object
has covered" during its motion.
b) Displacement is a vector quantity
which refers to “the overall change in
position of the object from start to finish”.
You can think of it as the distance “the
shortest distance that the crow flies”.
What is the car’s distance, what is
the car’s displacement?

The car covered a distance of 25 km
and a displacement of 10 km, East
What distance did Tim travel?
What was Tim’s displacment?

Tim covered a distance of (3m + 4m) = 5 m
and a displacement of 5 m, NE
What is the distance the physics
student travelled? What is their
displacement?
Example- A physics student walks 4 meters East, 2
meters South, 4 meters West, and finally 2 meters
North.
The student covered a distance of 12 m (4m +
2m + 4m +2 m) = 12 meters
and has a displacement of O m
Distance vs- Displacement
A football coach paces back and forth along the
sidelines- the coach moves from position A to B to C
to D. What is his distance covered and
displacement?
The coach covers a distance of (35 yds + 20 yds + 40
yds) = 95 yards
and has a displacement of 55 yards, left.
KAHOOT 1
1.2
Speed, and Velocity
Speed
Speed (s) – Rate at which an object is
moving.
 speed = distance / time
 s = d/t
 Like distance, speed does not depend on
direction.

Speed

A car drives 100 meters in 5 seconds.
1s
2
3
4
5
100 m

What is the car’s average speed?
s = d/t
 s = (100 m) / (5 s) = 20 m/s

Speed

A rocket is traveling at 10 m/s. How long does it
take the rocket to travel 30 m?
Speed

A racecar is traveling at 85.0 m/s. How far
does the car travel in 30.0 s?
Velocity
Velocity (v) – speed with direction.
 velocity = displacement / time
 v = d / t
 Has magnitude and direction!


Magnitude – a measure that has a value
Pulling It All Together

Back to our ant explorer!
- +
1s
2
3
4
5
0
cm
1
2
3
4
5
6
7
8
9
10
Distance traveled: 7 cm
 Displacement: +3 cm
 Average speed: (7 cm) / (5 s) = 1.4 cm/s
 Average velocity: (+3 cm) / (5 s) = +0.6 cm/s

Review

Is speed a vector
or scalar?

Scalar

Is distance a
vector or scalar?

Scalar

Is displacement a
vector or scalar?

Vector