Physics
Velocity: Instantaneous, Average, and vs. Time graph’s

Instantaneous velocity is a property of the object at a _single____ time; the average
velocity of the object depends on two times.

At any point, the slope of the position vs. time curve is the instantaneous velocity.

The velocity at two different times may have opposite signs, indicating that the object
changed directions.

When the acceleration is constant, the average velocity between two points lies
between the instantaneous velocities at each of the points.
VELOCITY is a vector quantity defined as the RATE OF CHANGE OF DISPLACEMENT. It is given the
symbol v and has units of metres per second (m/s) in a specified direction. You can express average
velocity in any units of time, but seconds are the international scientific standard (SI units).
AVERAGE VELOCITY may be defined as the total displacement divided by the time taken to make
that displacement, that is, v = Δd/Δt.
WORK this PROBLEM:
Velocities must be added by the methods used for the addition of vectors, for example:
A canoeist paddles across a river in a direction perpendicular to the flow with a speed of 1.5 m/s. The
current has a velocity 2 m/s parallel to the river bank. What is the resultant velocity of the canoe?
This problem may be solved by constructing a scale
diagram, but since the current and the direction
paddled are perpendicular to each other, it is easy to
solve it algebraically:
= tan-1 (1.5/2.0)
= 36.9°
The Meaning of Shape for a v-t Graph

Meaning of Shape for a v-t Graph
The use of velocity versus time graphs to describe motion. The first part of this lesson involves a study of the
relationship between the shape of a v-t graph and the motion of the object.
Constant Velocity versus Changing Velocity
Consider a car moving with a constant, rightward
(+) velocity - say of +10 m/s. A car moving with a
constant velocity is a car with zero acceleration.
If the velocity-time data for such a car were graphed, then the resulting
graph would look like the graph at the left. Note that a motion described as a
constant, positive velocity results in a line of zero slope (a horizontal line has
zero slope) when plotted as a velocity-time graph. Furthermore, only positive
velocity values are plotted, corresponding to a motion with positive velocity.
Now consider a car moving with a rightward (+),
changing velocity - that is, a car that is moving
rightward but speeding up or accelerating. Since the
car is moving in the positive direction and speeding
up, the car is said to have a positive acceleration.
If the velocity-time data for such a car were graphed, then the resulting
graph would look like the graph at the left. Note that a motion described as
a changing, positive velocity results in a sloped line when plotted as a
velocity-time graph. The slope of the line is positive, corresponding to the
positive acceleration. Furthermore, only positive velocity values are plotted,
corresponding to a motion with positive velocity.
The velocity vs. time graphs for the two types of motion - constant velocity and changing velocity (acceleration) - can be
summarized as follows.
Positive Velocity
Zero Acceleration
Positive Velocity
Positive Acceleration
The Importance of Slope
The shapes of the velocity vs. time graphs for these two basic types of
motion - constant velocity motion and accelerated motion (i.e., changing
velocity) - reveal an important principle. The principle is that the slope
of the line on a velocity-time graph reveals useful information
about the acceleration of the object.
If the acceleration is zero, then the slope is zero (i.e., a horizontal line).
If the acceleration is positive, then the slope is positive (i.e., an upward sloping line). If the acceleration is negative, then
the slope is negative (i.e., a downward sloping line). This very principle can be extended to any conceivable motion.
The slope of a velocity-time graph reveals information about an object's acceleration. But how can one tell whether the
object is moving in the positive direction (i.e., positive velocity) or in the negative direction (i.e., negative velocity)? And
how can one tell if the object is speeding up or slowing down?
Positive Velocity versus Negative Velocity
Speeding Up versus Slowing Down
Consider the graph below. The object whose motion is represented by this graph is ... (include all that are true):
a.
b.
c.
d.
e.
f.
g.
h.
moving in the positive direction.
moving with a constant velocity.
moving with a negative velocity.
slowing down.
changing directions.
speeding up.
moving with a positive acceleration.
moving with a constant acceleration.
Answers: a, d and h apply.
a: TRUE since the line is in the positive region of the graph.
b. FALSE since there is an acceleration (i.e., a changing velocity).
c. FALSE since a negative velocity would be a line in the negative region (i.e., below the horizontal axis).
d. TRUE since the line is approaching the 0-velocity level (the x-axis).
e. FALSE since the line never crosses the axis.
f. FALSE since the line is not moving away from x-axis.
g. FALSE since the line has a negative or downward slope.
h. TRUE since the line is straight (i.e, has a constant slope).
http://www.physicsclassroom.com/Physics-Interactives/1-D-Kinematics/Graph-That-Motion/GraphThat-Motion-Interactive