Physics 1A
Lecture 2A
"You must learn from the mistakes of others. You can't
possibly live long enough to make them all yourself."
--Sam Levenson
Motion
Chapter 2 will focus on motion in one
dimension.
Any description of motion involves three
concepts:
1) Displacement
2) Velocity
3) Acceleration
Displacement
Nearly the first thing you must do in every
Physics problem is define a coordinate system.
Choosing the proper coordinate system can make
a huge difference.
For one dimensional motion it is rather easy.
1) Choose an origin.
2) Choose a positive direction.
3) Stick to your choices throughout the problem!
Displacement
x is defined as the
position compared to the
origin.
x can be a positive or
negative value.
Displacement, ∆x, is a
difference between
positions.
∆x = x2–x1
∆x can be a positive or
negative value.
Displacement
Distance, d, is the total length travelled.
d can only be a positive value.
For many problems, we will be dealing with an
object in motion.
Thus, the position, x, will change with time, t.
We represent this with: x(t).
This means that the value of x depends on the
value of t that you choose.
Velocity
The velocity of an object is its displacement
over a period of time.
Average velocity, vavg, is:
Average velocity may be a positive or
negative value.
The speed of an object is its distance
travelled over a period of time.
Average speed is:
Average speed is only a positive value.
Velocity
Graphically, we find average velocity by examining
the rise (Δx) over the run (Δt) in an x vs. t graph
Between points A
and B, we find
that the average
velocity would be:
Velocity
Instantaneous velocity is the velocity at a given
instant of time.
Instantaneous velocity, v, is:
Instantaneous velocity can be a positive or
negative value.
Instantaneous speed will just be the
magnitude of the instantaneous velocity
(only positive).
We usually “drop” instantaneous when
talking about velocity or speed.
Velocity
Graphically, we find instantaneous velocity by examining
the slope of an x vs. t graph at a particular point.
It is different
from average
velocity in
that you do
not care what
happens over
a time period
only a time
instant.
Velocity
Example
You throw a ball up into the air to a height
of 1m and watch it drop back into your hand
after 2 seconds. What is the average
velocity and average speed of the ball over
the 2 second span? What is the
instantaneous velocity at t = 1s?
Answer
First, you must define a coordinate system.
Let’s choose up as positive, and sketch the
problem.
Velocity
Answer
Motion Graph
For average velocity:
1.2
height (in m)
1
0.8
0.6
0.4
0.2
0
0
0.5
1
time (in sec)
1.5
2
For average speed:
For velocity:
v = slope at t=1s = 0 m/s
Acceleration
The acceleration of an object is how much its
velocity changes over a period of time.
Average acceleration, aavg, is:
Average acceleration may be a positive or
negative value.
Instantaneous acceleration is the
acceleration of an object at a given
instant of time.
Acceleration is:
Acceleration may be a positive or negative value.
Acceleration
Acceleration is usually measured in units of m/s2.
But you can also find it in other units so be careful.
Watch out for the sign of acceleration.
Positive acceleration does not always mean “speeding
up.”
Nor does negative acceleration always mean “slowing
down.”
When acceleration and velocity are in the same
direction, the object “speeds up.”
When acceleration and velocity are in opposite
directions, the object “slows down.”
Acceleration
Motion diagrams are an excellent way to view the
relationship between velocity and acceleration.
Here velocity and acceleration are in opposite
directions.
Velocity is decreasing (red arrows are getting
shorter).
Positive velocity and negative acceleration.
Acceleration
Here velocity and acceleration are still in opposite
directions.
Velocity is increasing (getting less negative),
speed is decreasing (getting smaller).
Negative velocity and positive acceleration.
Kinematics
With the basic definitions now in place we
can turn to kinematics.
Kinematics is the study of motion.
A set of equations to describe a body in
motion has been derived known as the
kinematic equations.
These equations assume that the acceleration
of the body in motion is constant in time.
For Next Time (FNT)
Finish up the homework for
Chapter 1
Finish reading Chapter 2
Problem Solving Sessions will start
next week.