1. One Dimensional Motion
HONORS PHYSICS: Chapter 2 Notes
One Dimensional Motion
8/29/2014
Honors Physics
Fall, 2014
Cunnings, Fall, 2014

2. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Vector quantities
Anything with MAGNITUDE and DIRECTION is termed a vector quantity
Scalar quantities just have magnitude
Gravity propels a skier down a snow-covered slope at an acceleration approximately constant. The equations of “KINEMATICS”, as studied in this chapter, can give his position and velocity at any given time
Cunnings, Fall, 2014

3. Position, Distance, and Displacement
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Position, Distance, and Displacement
Coordinate system  defines position
Distance  total length of travel
(SI unit = meter, m)
Scalar quantity
Displacement  change in position
Cunnings, Fall, 2014

4. Position, Distance, and Displacement
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Position, Distance, and Displacement
Before describing motion, you must set up a coordinate system – define an origin and a positive direction.
The distance is the total length of travel; if you drive from your house to the grocery store and back, what is the total distance you traveled?
Displacement is the change in position. If you drive from your house to the grocery store and then to your friend’s house, what is your total distance?
What is your displacement?
Cunnings, Fall, 2014

5. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Cunnings, Fall, 2014

6. Average speed and velocity
HONORS PHYSICS: Chapter 2 Notes
Average speed and velocity
8/29/2014
Average speed = distance / time
Average velocity  displacement divided by the total elapsed time
Cunnings, Fall, 2014

7. Average speed and velocity
HONORS PHYSICS: Chapter 2 Notes
Average speed and velocity
8/29/2014
What’s his average velocity if he returns to his starting point?
What is his average velocity if he sprints 50 m in 8 s?
What’s his average velocity if he walks back to the starting line in 40 s?
Cunnings, Fall, 2014

8. Displacement and Velocity in One Dimension
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Displacement
Time taken
Displacement and Velocity in One Dimension
Cunnings, Fall, 2014

9. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Cunnings, Fall, 2014

10. Graphical Interpretation of Velocity
HONORS PHYSICS: Chapter 2 Notes
Graphical Interpretation of Velocity
8/29/2014
The left graph shows a car moving at constant velocity (linear). The graph on the right shows a car with changing velocity. The average velocity for a given time interval is the slope of the line connecting the two coordinates in question.
Cunnings, Fall, 2014

11. Graphical Interpretation of Average Velocity
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Graphical Interpretation of Average Velocity
The same motion, plotted one-dimensionally and as an position vs. time (x-t) graph:
Position vs time graphs give us information about:
average velocity  slope of a line on a x-t plot is equal to the average velocity over that interval
Cunnings, Fall, 2014

12. Graphical Interpretation of average velocity
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Graphical Interpretation of average velocity
What’s the average velocity between the intervals t = 0 s  t = 3 s? Is the velocity positive or negative?
What’s the average velocity between the intervals t = 2 s  t = 3 s? Is the velocity positive or negative?
Cunnings, Fall, 2014

13. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Which object is moving with constant POSITIVE velocity? Which is moving with NEGATIVE velocity? Which isn’t moving?
HOW DO YOU KNOW?
Cunnings, Fall, 2014

14. Instantaneous Velocity
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Instantaneous Velocity
Instantaneous velocity
This means that we evaluate the average velocity over a shorter and shorter period of time
Cunnings, Fall, 2014

15. Instantaneous velocity
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
If we have a more complex motion…
This plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity is the SLOPE OF THE LINE tangent to the curve.
Cunnings, Fall, 2014

16. Instantaneous velocity
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Average velocity is the slope of the straight line connecting two points corresponding to a given time interval
Instantaneous velocity is the slope of the tangent line at a given instant of time
Cunnings, Fall, 2014

17. Instantaneous velocity
HONORS PHYSICS: Chapter 2 Notes
Instantaneous velocity
8/29/2014
Is the
Instantaneous
velocity at t = 0.5 s
Greater than
Less than
Or equal to
the instantaneous velocity at t =1.0 s?
How do you know?
Cunnings, Fall, 2014

18. Displacement and Velocity in One Dimension
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Displacement and Velocity in One Dimension
Are the plots shown at the left correctly related
A) YES B) NO
CAN YOU EXPLAIN WHY?!?!
THERE’S ROOM OVER THERE 
YOU KNOW…
Cunnings, Fall, 2014 18

19. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
The velocity vs. time plot of some object is shown to the right. Which diagram below could be the Displacement vs. time plot for the same object? A B C
Cunnings, Fall, 2014 19

20. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Acceleration
Average acceleration  the change in velocity divided by the time it took to change the velocity
Cunnings, Fall, 2014

21. HONORS PHYSICS: Chapter 2 Notes
Acceleration
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
On Earth, gravitational acceleration equals about 10 m/s/s
What does it mean to have an acceleration of 10 m/s2 ?
Time (s)
Velocity (m/s) 1 10 2 20 3 30
Cunnings, Fall, 2014

22. Graphical interpretation of Acceleration
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Graphical interpretation of Acceleration
Cunnings, Fall, 2014

23. Important Point Regarding Acceleration
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Important Point Regarding Acceleration
When an object’s velocity and acceleration (both vector quantities) occur in the same direction, the object is SPEEDING UP!!!!
When an object’s velocity and acceleration occur in opposing directions, the object is SLOWING DOWN!!!
Deceleration is used to refer to a decrease in speed
Don’t confuse “negative acceleration” with deceleration…PLEASE!!
Cunnings, Fall, 2014

24. Instantaneous Acceleration
HONORS PHYSICS: Chapter 2 Notes
Instantaneous Acceleration
8/29/2014
Very similar to “instantaneous velocity” from our position vs. time graphs
a = lim Δv / Δt
t0
The closer Δt gets to zero, the closer our ratio gets to a fixed number.
Cunnings, Fall, 2014

25. HONORS PHYSICS: Chapter 2 Notes
Acceleration
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Cunnings, Fall, 2014 25

26. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Cunnings, Fall, 2014

27. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Velocity vs time (v-t) graphs give us information about: average acceleration, instantaneous acceleration
the “+” 0.25 m/s2 means the particle’s speed is increasing by 0.25 m/s every second
Cunnings, Fall, 2014

28. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time? A B
Cunnings, Fall, 2014 28

29. 1-D Motion with constant acceleration
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
1-D Motion with constant acceleration
When an object moves at constant acceleration, the instantaneous acceleration at any point in a time interval equals the average acceleration divided by the whole time interval
In other words, with constant acceleration:
Average acceleration is no different than instantaneous acceleration!
Cunnings, Fall, 2014

30. Motion with constant acceleration
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Motion with constant acceleration
If the acceleration is constant, the velocity changes linearly:
Average velocity:
v0 = initial velocity
a = acceleration
t = time
Cunnings, Fall, 2014

31. Constant Acceleration
HONORS PHYSICS: Chapter 2 Notes
Constant Acceleration
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constant a(t) = a
Cunnings, Fall, 2014 31

32. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Finding Displacement on a graph not using the origin as initial coordinates
What this graph shows is the geometrical interpretation of the following equation! Cool, huh?!
Cunnings, Fall, 2014

33. Freely Falling Objects
HONORS PHYSICS: Chapter 2 Notes
Freely Falling Objects
8/29/2014
All objects fall towards earth at the same constant acceleration
Assuming air resistance is zero, of course!!
Any object moving upward, downward, or released from rest under the influence of gravity is considered “free falling”
A football in the air, skydiver, falling book, etc.
Cunnings, Fall, 2014

34. Motion with constant acceleration
HONORS PHYSICS: Chapter 2 Notes
8/29/2014
An object falling in air is subject to air resistance (and therefore is not freely falling).
Free fall is the motion of an object subject only to the influences of gravity…in most cases we’ll consider, air resistance is negligible and can be ignored.
Cunnings, Fall, 2014

35. HONORS PHYSICS: Chapter 2 Notes
8/29/2014
Free falling objects
Free fall from rest:
You could use the
kinematics equations
to see where the
numbers are coming
from, fyi!!!
Cunnings, Fall, 2014

36. Trajectory of a projectile
HONORS PHYSICS: Chapter 2 Notes
Trajectory of a projectile
8/29/2014
Cunnings, Fall, 2014