DISTANCE VS
DISPLACEMENT
SPEED VS VELOCITY
DISTANCE – scalar quantity
DISPLACEMENT – vector quantity
A car travels 50 km to the East and then 20
km to the West, the total distance traveled
is 70 km, but your displacement is 30 km
East.
E
Representing Displacement



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Let x1 be position of object at time t1
Let x2 be position at time t2
Then displacement Dx = x2 – x1
D (Greek letter delta) means change
If a person starts at x1 = 40m and walks to the left until
reaching x2 = 10m what is the displacement?
Answer: Dx = x2 – x1 = 10m – 40m = -30m
Average Speed and Velocity
Velocity is speed and direction
Average speed = distance traveled ÷ time
elapsed
Average velocity = displacement ÷ time
elapsed
Not always equal
Find average speed and velocity for a trip 60m North followed
by 40m South in 10 seconds.
Answers: 10 m/s; 2 m/s N
Velocity shows how fast an object is moving
in a certain direction.
Average velocity can be calculated by
dividing TOTAL displacement over TOTAL
time.
.
(Ex) A car moved 50 km in 2 hours. The
average velocity is 25 km/h because
Example
During a four second interval a runner’s
position changes from x1 = 50m to x2 = 10m.
What was the average velocity?
vav = Dx/Dt = x2 – x1 = -40m/4s = -10 m/s
What is the average speed in kph?
-10 m/s x 1 km/1000m x 3600 sec/ 1h = -36 km/h
INSTANTANEOUS VELOCITY
Velocity at a
particular instant
of time.
Defined as average
velocity over an
infinitesimally
short time
interval
INSTANTANEOUS VELOCITY
The instantaneous velocity shows the velocity
of an object at one point. For example, the
speedometer of a car traveling along the
autobahn (German freeway) swings to 200
km/h, indicates that the instantaneous
velocity of the car is 200 km/h.
QUESTION: A car moved 20 km East
and 60 km West in 2 hours. What is its
average velocity in kph ?
V ave = total displacement
total time
= 20 km – 60 km
2h
= - 20 kph or
20 kph W (negative indicates
western direction)
QUESTION: How far (in km) will a
car travel in 15 min at 20 m/s ?
d=vt
= (20 m) (60 s) (15 min)
s
min
= 18 000 m
= 18 km
Distance with constant velocity
How far could a runner
traveling at an average
speed of 36 km/h go in 20
minutes?
20 min = 1/3 hour
Dx = vav Dt = 36 km/h x 1/3h
= 12 km = 1.2 x 104 m
Position-time graph simply shows the relationship
between time and position. From the following
data, for example,
time (s)
position
(m)
0
1
2
3
4
5
0
20
50
130
150
200
You can draw the following graph
The tangent of a positiontime graph represents
velocity since
A velocity-time graph shows the relationship
between velocity and time. For example, if a car
moves at constant velocity of 5 m/s for 10
seconds, you can draw a velocity-time graph that
looks like this:
The area below the line represents the displacement
the object traveled since it can be calculated by
xy, or (time X velocity) which equals to
displacement.