•
The usual practice is to
graph distance versus
time, which puts distance
on the vertical axis.
•
Note that the data points
lie on a straight line.

1.4 Simple Types of Motion
•
Remember this simple rule for the relationship
between distance and time:
when the
speed is constant,
the graph of
distance versus time is a
straight line.
•
In general, when one quantity is
proportional
to
another, the graph of the two quantities is a straight
line.

1.4 Simple Types of Motion
•
An important feature of this graph is its
slope.
•
The slope of a graph is a measure of its steepness.
•
In particular, the slope is equal to the
rise
between
two points on the line divided by the
run
between
the points.

1.4 Simple Types of Motion
•
This is illustrated in the figure shown.
•
The rise is a distance,
d
, and the run is a time
interval,
t
.
•
So the slope equals
d
divided by
t
, which is
also the object’s
velocity
.
•
The slope of a distance-
versus-time graph
equals the velocity.

1.4 Simple Types of Motion
•
Even when the velocity is not constant, the slope
of a
d
versus
t
graph is still equal to the velocity.
•
In this case, the graph is not a straight line
because, as the slope changes (a result of the
changing velocity), the
graph curves or bends
.
•
Indicates acceleration
.

1.4 Simple Types of Motion
•
The graph shown represents the motion of a car
that starts from a stop sign, drives down a street,
and then stops and backs into a parking place.
aVsTime/xVsTime.html
Interactive tool – position vs. time graph

1.4 Simple Types of Motion
Constant Acceleration
•
Let’s use free fall as our example.
•
Assume that a heavy rock is dropped from the top
of a building and that we can measure the
instantaneous velocity of the rock and the distance
that it has fallen at any time we choose.
•
The rock falls with an acceleration equal to
g =
9.8 m/s
2

1.4 Simple Types of Motion
Constant Acceleration

1.4 Simple Types of Motion
Constant Acceleration
•
First, consider how the rock’s velocity changes.
The velocity increases 9.8 m/s, each second.
•
Mathematically,
v
(m/s)
= 9.8 (m/s
2
) x
t
(s)
The general form of the
equation that applies to any object that starts from
rest and has a constant acceleration
a
is
v
=
at
(when acceleration is constant)

1.4 Simple Types of Motion
Constant Acceleration
•
Review: the graph of
distance
versus time is a
straight line for constant velocity (uniform motion).
•
For constant acceleration, the graph of
velocity
versus
time
exhibits a linear behaviour
.

1.4 Simple Types of Motion
Constant Acceleration
•
What is the relationship between
distance and time when the
acceleration is constant?
•
It is a bit more complicated, as
expected.
•
The figure shows that the distance a
falling body travels during each
successive time interval grows larger
as it falls.
•
Because the velocity is continually
changing, the distance equals the
average velocity
multiplied by the
time.

1.4 Simple Types of Motion
Constant Acceleration
•
What is the average velocity?