1. Chapter 2:Motion along a straight line
Translational Motion and Rotational Motion
Today
Later

2. Current information
1. Please read carefully all the instructions on the coursewebsite
2. The problems in the syllabus are the same as in
Mastering Physics on the web.
3. Have a notebook, solve the problems first and then submit
them on Mastering Physics site.
4. There are due dates for the problems on Mastering Physics,
so don’t procrastinate.
5. Enroll in WebAssign, since all tasks for the labs are given
and submitted through this system. Prelab part is due 15 min before
the start of the recitation.

3. Modified Mastering Physics Course: schuessler29324
Settings in Mastering Physics:
4 attempts are given (no subtractions within this attempts),
after 4 attempts – no credit. Sometimes need use reset button.
Graded tutorials are due soon after the lecture.
Other problems are due on the date of the respective exam.
Practical hint: perform calculations to 4 sign. figures
and round as needed.

4. Describing Motion … Coordinates  Position (displacement)  Velocity
 Acceleration
a) Motion with zero acceleration
b) Motion with non-zero acceleration

5. Kinematics in One Dimension: Displacement

6. Average speed and velocity
Average velocity = total displacement covered
per total elapsed time,
Speed is just the magnitude of velocity!
The “how fast” without accounting for the direction.
Average speed = total distance covered per total elapsed time,
Instantaneous velocity, velocity at a given instant

7. Average velocity

8. Instantaneous velocity

9. Graphic representation: Velocity
Slope is average velocity during t=t2-t1
Slope is instantaneous velocity at t1

10. The figure shows x versus t graphs for four cars (A–D) moving on a straight road. The x axis is aligned with the road. Decide which car, if any, satisfies each of the following questions. Choose E if none of the cars satisfies the question. Which car reverses direction? Which car is slowing down?
Which car reverses direction?
Which car is speeding up?
Which car is not moving?
Which car moves in the -x direction?
Answer: e)
© 2016 Pearson Education, Inc.

11. Engine traveling on rail

12. Acceleration
We say that things which have changing velocity are “accelerating”
Acceleration is the “Rate of change of velocity”
You hit the accelerator in your car to speed up
(Ok…It’s true you also hit it to stay at constant velocity, but that’s because friction is slowing you down…we’ll get to that later…)

13. Average acceleration Unit of acceleration: (m/s)/s=m/s2
Meters per second squared

14. Average Velocity For constant acceleration
The area under the graph v(t)
is the total distance travelled v
vav v0 t Dt

15. Kinematics in one dimension
Motion with constant acceleration.
From the formula for average acceleration
We find
On the other hand
Then we can find

16. Recap
So for constant acceleration we find: x t v t a t

17. Examples
Can a car have uniform speed and non-constant velocity?
Can an object have a positive average velocity over the last hour, and a negative instantaneous velocity?

18. Conceptual Example
If the velocity of an object is zero, does it mean that the acceleration is zero?
Example?
If the acceleration is zero, does that mean that the velocity is zero?

19. Example of graphic solution: Catching a speeder
m/s

21. Kinematics equations for constant acceleration

22. All objects fall with the same constant acceleration!!

23. Testing Kinetics for a=9.80m/s2
Experiments on the motion of objects falling from leaning tower of Pisa
under the action of the force of gravity

24. Acceleration of gravity on different planets, =9.81m/s2

25. A brick is dropped from the roof of a building
The brick strikes the ground after 5s. (Sign convention does not matter!)
How tall?
Velocity of brick just before it strikes the ground?
Choose + upward:
Choose + downward:
Important to have the
correct interpretation
of the results!
The optimal selection
of the reference frame helps.

26. Problem: Vertical motion
Stone is thrown vertically upward

27. Ball thrown upward How high? How long in the air?
How high?
at point A:
How long in the air?
How long for highest point?
height of the cliff h=50m

28. Ball thrown upward (cont.)
Velocity when ball reaches the thrower’s hand?
At what time does the ball pass a point 8m above the throwers hand =
How long does it take to reach the base of the cliff and what is the velocity there? (h = 50m)
t1 = (15 + (15^2 + 4*4.9*50)^0.5)/(2*4.95) = = 5.07 s
t2 = (15 - (15^2 + 4*4.9*50)^0.5)/(2*4.95) = = s

29. 1-D motions in the gravitational field

30. Clicker problem
When you brake on dry pavement, your maximum acceleration is about three times greater than when you brake on wet pavement. For a given initial speed, how does your stopping distance xdry on dry pavement compare with your stopping distance xwet on wet pavement?
a) xdry = 1/3xwet b) xdry = 3xwet c) xdry = 1/9xwet d) xdry = 9xwet
Answer: a) xdry = 1/3xwet
© 2016 Pearson Education, Inc.

31. Average Velocity (example)
x (meters) 6 4 2
t (seconds) -2 1 2 3 4
What is the average velocity over the first 4 seconds ?
A) -2 m/s
B) 4 m/s
C) 1 m/s
D) not enough
information to
decide.

32. Instantaneous Velocity
x (meters) 6 4 2 -2
t (seconds) 1 2 3 4
What is the instantaneous velocity at the fourth second ?
A) 4 m/s
B) 0 m/s
C) 1 m/s
D) not enough
information to
decide.