Chapter 2 Homework #1
Questions: 2,3,4,5,6,9,16, 17
Problems: 1,2,5,6,9,8,13, 17,
20,22,23,26, 27,28
Due Sept 29
Quiz on Section 1-6 on Sept 29
September 14
Physics Ch. 2 Motion in One
Dimension
Section 1-4 Notes
Velocity & Displacement
Mechanics

The study of the motion of objects
– Kinematics: the description of how objects move
– Dynamics: forces and why objects move the way they do
– Translational motion: objects moving without rotating
Module 2-1
Reference Frames

Module 2-1
Any measurement of position, displacement,
velocity or acceleration must be made with
respect to a defined reference frame
Coordinate System

Determine your reference frame, then set up a
coordinate system
+y
+y
+x
+x
Module 2-1
Displacement

Displacement = change in position
Displacement is not always equal to the distance traveled
Δx = x2 – x1
Δx
Displacement is
positive:
Displacement is
negative:
Right
Left
Up
Down
Velocity

A vector representing displacement occurring in
a certain time interval
Average velocity = change in position = displacement
change in time
time interval
vavg = Δx = x2 – x1
Δt
t2 – t1
Speed

Speed is the distance traveled in a certain
time (direction is of no consequence)
Δx

If this motion took 10s, which would be
greater here, velocity or speed?
Graphing Velocity

Velocity can be determined by the slope of
a line on a time vs. position graph
Position (m)
Velocity
14
12
10
8
6
4
2
0
0
2
4
Time (s)

Slope = rise/run = Δy/Δx
6
8
Instantaneous Velocity
The velocity of the object at one instantaneous moment
Velocity
can be different from
average velocity
70
Position (m)

60
50
40
30
20
10
0
Slope of the
0
2
4
6
tangent = velocity
Time (s)
 Instantaneous velocity and speed are the same value
because distance = displacement when instantaneous
 AP Physics equation sheet calls v speed

8
Acceleration
Acceleration is the rate of change of velocity.
Acceleration

The change in velocity over time
a = v2-v1
Δt
Acceleration is a vector, although in one-dimensional
motion we only need the sign.
Positive acceleration – acceleration in the direction of
motion.
Negative acceleration – acceleration opposite the direction
of motion (decelerating)
Exception to above:
Acceleration is positive
because direction of motion
is negative
Practice Problems
2-1. The position of a runner as a function of time
is plotted as moving along the x axis. During a
3.00s time interval, the runner’s position changes
from x1=50.0m to x2=30.5m. What was the
runner’s average velocity?
Practice Problems
2-2. How far can a cyclist travel in 2.5h along a
straight road if her average speed is 18 km/h?
2-4. A car accelerates along a straight road from
rest to 75km/h in 5.0s. What is the magnitude of
the average acceleration?
Practice Problems
2-5. a) If the velocity of an object is zero, does it
mean the acceleration is zero? Think of a situation
to support your claim.
2-5. b) If the acceleration is zero, does it mean the
velocity is zero? Think of a situation to support
your claim.
Practice Problems
2-6. An automobile is moving to the right along a
straight highway, which we choose to be the
positive x axis, and the driver puts on the breaks.
If the initial velocity is 15.0m/s and it takes 5.0s to
slow down to 5.0m/s, what was the car’s average
acceleration?
September 15
Physics Ch. 2 Motion in One
Dimension
Don’t write the
info in red font
Section 5-6 Notes
Acceleration
Acceleration
Acceleration is a measure of the rate of
change in velocity
 The change in velocity can be a change in
the speed or in the direction

Ex. Units: m/s2, mi/hr/s, km/hr/s
Graphing Acceleration
The slope of a time vs. velocity graph equals the
acceleration
Acceleration
14
Velocity (m/s)

12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
Time (seconds)
9
10 11 12 13
Uniform Acceleration
When acceleration is constant
 Example: acceleration from
gravity is a constant 9.8m/s/s

Acceleration
Velocity (m/s)
50
40
30
20
10
0
0
1
2
3
Time (seconds)
4
5
Displacement, again

Displacement depends on acceleration, initial
velocity and the time
Final Velocity

Final velocity depends on initial velocity,
acceleration and time
-or-
Average Velocity (not on equation sheet)
Solving Problems
1. Read the whole problem and make sure you
understand it. Then read it again.
2. Draw a diagram and choose coordinate axes.
3. Write down the givens and unknown (known
quantities), and then the unknown ones that
you need to find.
2-6 Solving Problems
4. Choose the appropriate equation based on
your givens. Write down the equation(s).
5. Insert the givens (with units!!!) into equations
6. Solve algebraically keeping track of units and
canceling when appropriate
7. Round answer using sig fig rules
8. Look at the result – is it reasonable? Does it
agree with a rough estimate?
9. Check the units again.
An airplane accelerates along a 1.5km
runway. It starts at rest and then reaches a
velocity of 50.0m/s before taking off. What
is its acceleration?
Practice Problems
2-7. You are designing an airport for small planes.
One kind of plane that might use this airfield must
reach a speed before take off of at least 27.8m/s
(100km/h), and can accelerate at 2.00m/s2. (a) If
the runway is 150m long, can this airplane reach
the proper take off speed? (b) If not, what
minimum length must the runway have?
2-8. How long does it take a car to cross a 30.0m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00m/s2?
2-9. Estimate the minimum stopping distance for a
car that is traveling 50 km/h and has an
acceleration of -6.0m/s2 once the brakes are
applied. Take into account the driver’s reaction
time of 0.50s during which time the car has an
acceleration of zero.
Chapter 2 Homework #2
Questions: 7,8,11
Problems: 7,12,18,24,29,31,
39,40,41,42,45,46,49
General Problems: 60
Misconception Questions 1-9
Due Oct 1? Chapter 2 Test on Oct 2?
September22
Physics Ch. 2 Motion in One
Dimension
Section 7 Notes
Falling Objects
Near the surface of the Earth, all objects
experience approximately the same acceleration
due to gravity.
This is one of the most
common examples of
motion with constant
acceleration.
Galileo’s Hypothesis
In the absence of air
resistance, all objects
fall with the same
acceleration, although
this may be hard to tell
by testing in an
environment where
there is air resistance.
Feather drop video
The acceleration due to
gravity at the Earth’s
surface is approximately
9.80 m/s2.
Free Fall
Objects in free fall undergo a constant acceleration from
gravity
All the same kinematic equations
apply, you can insert y in
wherever there is an x

What goes up, must come down
Objects thrown upwards undergo a constant
negative acceleration from gravity
 At the peak of their upward path, velocity is
zero, then
Acceleration
the object
60
accelerates
40
20
downward
0
 The up trip
1
2
3
4
5
6
7
8
-20 0
-40
and down trip
-60
take the same
Time (seconds)
amount of time
Velocity (m/s)

9
Practice Problems
2-10. Suppose that a ball is dropped from a tower.
How far will it have fallen after 1.00s, 2.00s and
3.00s? Assume y is positive downward. Neglect
air resistance.
Practice Problems
2-11. Suppose a ball is thrown downward with an
initial velocity of 3.00m/s off the tower. (a) What
would its position be after 1.00s and 2.00s? (b)
What would its speed be after 1.00s and 2.00s?
(c) Compare your answers in (b) to the speed of a
ball that was dropped rather than thrown.
Practice Problems
2-12/13. A person throws a ball upward into the
air with an initial velocity of 15.0m/s. Calculate (a)
how high the ball goes and (b) how long the ball is
in the air before it comes back to his hand.
Neglect the throwing action, we only care about
after the ball leaves the hand.
Practice Problems
2-14. Explain the error in these two common
misconceptions: (a) that acceleration and velocity
are always in the same direction, and (b) that an
object thrown upward has zero acceleration at the
highest point.
Homework Due: Oct ?
Test: Oct ?