Lesson 1
Review of Kinematics
Mechanics
The study of motion, and the related concepts of force and
energy is called Mechanics.
Mechanics is divided into two branches:
a) Kinematics – the study of how objects move
b) Dynamics- the study of the forces producing motion and
why objects move as they do
- 4 fundamental forces, gravity,
electromagnetism, strong nuclear force, weak
nuclear force
Kinematics
Describing how an object moves can be done in the following three
ways:
1) Words:
uniform motion, non-uniform motion, accelerating,
decelerating, fast, slow
2) Equations/Formulae/Formulas:
Words
Uniform Motion
Motion in a straight line at a constant speed, a=0
Non-Uniform Motion
Motion involving changes in speed and direction or both
Position
The distance between an object and a reference point, d
(arrow indicates vector quantity)
Displacement
The change in position of an object (change is shown with a
Δ -delta)
Displacement vs. Distance
Figure P.1a
Scalars vs. Vectors
-Impuse (kgm/s)
-momentum (kgm/s)
Instantaneous Velocity
Velocity at an instant in time
Figure P.1a
Words
Average velocity is total displacement divided by total time
and it takes in to account that velocity is not always uniform
during travel, at times, an object can speed up or slow down or
even stop
Be careful, average velocity is not the calculation of an average
but indicates the velocity over an entire period of travel
The formula is the same as that for instantaneous velocity but
with a modification
The notation v is used in
place of vavg and is said as
v bar
Figure P.1a
Instantaneous and Average Speed
Speed is defined as distance travelled over a time interval
Speed is a scalar, no vector notation is necessary
Speed can also be instantaneous or average just like with
velocity
Instantaneous speed is
v =
𝑑
𝑡
vavg =
𝑑
𝑡
 Average speed is
Figure P.1a
Units for velocity and Speed
𝑚
𝑘𝑚
 Units are most often 𝑠 , ℎ but other units can also be used
 These units are considered derived units because they consist of 2 of the base units (m,
and seconds)
𝑚
 We will also see how we can convert from 𝑠 𝑡𝑜
𝑘𝑚
and vice versa
ℎ
Direction for Vectors
 Direction is based on the cartesian plane, which involves the intersection of two
number lines
 Motion along the x axis, can be considered right or left or it can be considered motion
east or west or motion positive or negative
 Motion along the y axis can be considered north or south, positive or negative
 Square brackets are used to show direction, for example east is [E], south is [S] etc.
Graphical Analysis
Once a graph is made it can be analyzed in three ways
1) Read – Interpolate (reading inside the data range)
-Extrapolating (outside the data range)
2) Calculate the rate of change - SLOPE
3) Calcuate the AREA
Figure P.1a
Graphical Analysis
 Recall, graphical analysis also involves the calculation of
Area, in addition to calculating slopes and reading a graph
 The area of an acceleration-time graph is velocity
 The area of velocity-time graph is displacement
Graphs
These graphs look
different but they
show the exact same
motion
Average Velocity
 Position time graphs can be curved which indicates non-uniform
motion
 Non-uniform motion involves changes in speed, direction or
both
 Recall, average velocity takes into account that an object may have
sped up or slowed or even stopped in its travel, it is not the
calculation of an average
 By determining total displacement divided by the total time,
average velocity can be calculated.
 Average Velocity can be determined from a graph by
calculating the slope of a SECANT
 A SECANT is simple a line connecting two points, over a
time interval.
Secant
 Slope of a secant on a position-time graph represents average velocity (speed on a
distance-time graph)
 Select any two points on the secant line to find the slope
 x is often used to represent position or distance but we will not use this notaton.
Instantaneous Velocity
Instantaneous velocity is the velocity at a particular instant
in time
To determine instantaneous velocity, calculate the slope
of a TANGENT
A TANGENT is a line that touches only one point on a graph
If a graph is a straight line, then the terms average or
instantaneous are not necessary since they will yield the
same answer which is simple the velocity.
The slope of the tangent is equal to the slope of the curve at
that point.
Tangent
How to Draw a Tangent?
Drawing a tangent can be tricky
Consider the graph below, where the instantaneous velocity at A is to
be determined.
Look at the correct tangent line drawn
Describe how a proper tangent line is drawn
Notice the tangent has the slope of the point and just grazes it
without cutting through the curve
Figure P.1a
Acceleration
 Acceleration is the rate of change of velocity
 Therefore, it is the slope of a velocity-time graph
 Units are m/s/s,
𝑚
-2
2 , ms
𝑠
𝑚
 The unit indicates the change in velocity ( ) for every second
𝑠
 It is said as metres per second per second
 Acceleration is a vector quanity
 If velocity changes steadily then it is said to be uniformly
acceleration motion
 If velocity changes at a varying rate then acceleration is said to be
non-uniform acceleration
Acceleration and Velocity Direction
Velocity –Time Graph of Uniform and Non-Uniform
Acceleration
STEPS:
Drawing a Displacement-Time Graph from a
Velocity Time Graph
Graphs with Multiple Sections
 To calculate displacement from a velocity-time graphs with multiple sections, break
the graph into sections and find the area of each section and then add the areas up
Relationships of Graphs with One Another
The Big 5 Kinematic Equations
 To use these equations acceleration must be present
 Acceleration must be uniform
 Be careful with the use of these previous kinematic equations:
∆𝑑
𝑣=
∆𝑡
or
These equations above
can only be used if there
is NO acceleration
Kinematic Equations
Sample Problems
Sample Problems
Sample Problems Answers
Sample Problems Answers
Sample Problems Answers