Velocity vs. Speed
Velocity is a vector quantity and is defined as the change in an
object’s position per unit of time.
Velocity and speed are not the same thing and quite often
have different values.
Speed is a scalar quantity and is defined as the distance
travelled by an object per unit of time.
3 km [South]
2 km [North]
Remember Victor, he walked 5 km North to his friends house
in 2 hours and then 2 km South to Starbucks in 1 hour. What
was Victor’s average velocity and speed?
s 7 km
v = 2.3 km/hr
t 3 hr
s 3 km [N]
v = 1 km/hr [N]
t 3 hr
0 1 2 3 4
Velocity from Position-Time Graphs
Velocity can be determined from the slope of a line drawn on a
position time graph. For Victor’s walk:
A line can be drawn between Victor’s start and finish points
The slope value is the average
velocity 3 km [N]
Slope = 1 km/hr [N]
The average velocity for the entire trip shown in this
position-time graph is ZERO! Why?
TIP: Don’t confuse average velocity with a mean value
calculation we are not adding up a number of velocity
measurements and dividing by the number.
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Straight lines on a position-time graph indicate uniform
motion (CONSTANT VELOCITY). A change in slope or a
curved line indicate that velocity is changing. Any object that
undergoes a velocity change is experiencing an
graph shows the
velocity increase of a
falling ball. In this case,
the increase in velocity
implies an acceleration.
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One way to determine the velocity from this graph is to
calculate the slope of tangent lines. The slope of a tangent
indicates the INSTANTANEOUS velocity at that instant in
Velocity at t = 2 s
Velocity at t = 8 s
The slope of a tangent can be difficult to determine accurately.
Fortunately there is an easier way.
For objects that are accelerating uniformly, the
instantaneous velocity at the middle of a time interval is
the same as the average velocity for the time interval. On
a graph this looks like this
The average velocity of the time interval t = 2 6 s can be
determined by the slope of the red line.
t = 4 s
t = 2 s
t = 6 s
vavg 2-6 s= vinst 4 s
4 seconds is halfway through the
time interval of 2 6 s. The
instantaneous velocity at t = 4 s is the
same as the average velocity for the
SLOPES ARE PARALLEL
vavg 3-5 s= vinst 4 s
A velocity-time graph shows how the velocity of an object
changes with time.
This position-time graph
shows an object moving
away from a reference
point at a constant velocity.
How do we know?
This velocity-time graph
corresponds to the same
object. Note constant
velocity (how is this
What would the corresponding velocity-time graph be for a
ball being tossed in the air?
A car at rest (0 ms-1) increases its velocity by 1 ms-1 each
second. What would the velocity-time graph look like?
What would the slope of
this graph tell us?
The slope would give us the rate of change of the velocity
(units would be ms-1/s i.e. meters per second per second
or ms-2). The rate that velocity changes with time is called
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Practice: Calculate the velocity of this object in each distinct
section of the following position-time graph.
1 2 ms [N]v
2 0 msv
3 2.5 ms [S]v
4 0 msv
5 4.4 ms [N]v