Bellringer

1
Bellringer
Compare and explain in complete sentences
what is distance.
2
Previous homework
Graph your motion distance, velocity, and
acceleration for your travel on a bus/car
from home to school and back
3
Homework
CALCULATE DISTANCE, VELOCITY AT ANY TIMEFOR
THE ARROW SHOOT VERTICALLY IN THE AIR
4
Graphing Motion
Every Picture Tells A Story
5
Position Time Graphs of Accelerated motion
Position vs. time graphs give you an easy and
obvious way of determining an objects
displacement at any given time, and a subtler way
of determining that objects velocity at any
given time.
6
A very useful aspect of these graphs is that the
area under the v-t graph tells us the distance
travelled during the motion.
7
Since the slope represents the speed, if the
speed is increasing over time, the slope must be
also be increasing over time. The graph is a
curve that gets steeper as you move along The
x-axis. A position-time graph for a ball in
free fall is shown below.
8
The graph of an object slowing down is also
cuved. The example below show the position-time
graph for a car coming to a gradual stop at a red
l ight. As time passes, the cars speed
decreases. The slope must therefore decrease.
9
(No Transcript)
10
answers
11
Velocity vs Time Graphs
12
If the graph is a horizontal line, there is no
change in velocity, therefore there is no
acceleration (the slope is 0).
If the acceleration is positive then the slope is
positive (the line moves upward to the right).
If the acceleration is negative, then the slope
is negative (the line moves downward to the
right).).
13
Calculating acceleration from a velocity-time
graph
14
Calculating the distance on velocity-time graph.
15
An object is moving in the positive direction if
the line is located in the positive region of the
graph (whether it is sloping up or sloping down).
An object is moving in the negative direction if
the line is located in the negative region of the
graph (whether it is sloping up or sloping down).
If a line crosses over the x-axis from the
positive region to the negative region of the
graph (or vice versa), then the object has
changed directions.
16
The object moves in the direction at a constant
speed - zero acceleration (interval A). The
object then continues in the direction while
slowing down with a negative acceleration
(interval B). Finally, the object moves at a
constant speed in the direction, slower than
before (interval C).
17
The object moves in the direction while slowing
down this involves a negative acceleration
(interval A). It then remains at rest (interval
B). The object then moves in the - direction
while speeding up this also involves a negative
acceleration (interval C).
18
The object moves in the direction with a
constant velocity and zero acceleration (interval
A). The object then slows down while moving in
the direction (i.e., it has a negative
acceleration) until it finally reaches a 0
velocity (stops) (interval B). Then the object
moves in the - direction while speeding up this
corresponds to a - acceleration (interval C).
19
a plot of velocity versus time can also be used
to determine the displacement of an object. The
diagram below shows three different velocity-time
graphs the shaded regions between the line and
the time-axis represents the displacement during
the stated time interval.
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
The velocity-time graph for a two-stage rocket is
shown below. Use the graph and your understanding
of slope calculations to determine the
acceleration of the rocket during the listed time
intervals. When finished, click the buttons to
see the answers.
20 m/s2
40 m/s2
-20 m/s2
24
Constant positive (rightward) velocity
25
Constant negative (leftward) velocity
26
Rightward velocity with rightward acceleration.

27
Rightward Velocity and negative acceleration
28
Leftward velocity, leftward acceleration
29
Leftward velocity rightward acceleration
30
Acceleration

• Acceleration the rate at which velocity is
  changing
• Acceleration ?v/ ?t
• Can increase or decrease (sometimes called
  deceleration)
• Think of traveling in a car, you can feel the
  acceleration
• 3 ways to accelerate in a car
• Brake pedalslowing down coming to a stop
  (changing speed)
• Steering wheelgoing around a corner or curve
  (changing direction)
• Gas pedalleaving from a stopped position
  (changing speed)

31
(No Transcript)
32
The object moves in the direction at a constant
speed - zero acceleration (interval A). The
object then continues in the direction while
slowing down with a negative acceleration
(interval B). Finally, the object moves at a
constant speed in the direction, slower than
before (interval C).
33
The object moves in the direction at a constant
speed - zero acceleration (interval A). The
object then continues in the direction while
slowing down with a negative acceleration
(interval B). Finally, the object moves at a
constant speed in the direction, slower than
before (interval C).
34
The object moves in the direction while slowing
down this involves a negative acceleration
(interval A). It then remains at rest (interval
B). The object then moves in the - direction
while speeding up this also involves a negative
acceleration (interval C).
35

• Zero to 90s - On this graph we see a horizontal
  line that reads 5m/s for those same first 90
  seconds.
• On a v-t graph a flat line means constant
  velocity. Constant velocity means zero
  acceleration.

36
(No Transcript)
37
Graphs of MotionUniform Velocity

• The area under a velocity vs time graph is the
  displacement of the object.
• Find the distance traveled by each object.

38
Acceleration

• Suppose you are traveling in a car and your speed
  goes from 10.km/h to 60.km/h in 2.0s. What is
  your acceleration?
• Suppose a car goes from 80.km/h to 15km/h in 5.0
  seconds. What is the acceleration?
• A car is coasting backwards down a hill at a
  speed of 3.0m/s when the driver gets the engine
  started. After 2.5s, the car is moving uphill at
  4.5m/s. Assuming that uphill is in the positive
  direction, what is the cars average
  acceleration?

39
Graphs of Motion

• Velocity vs time graphs How can you tell if the
  object is accelerating or decelerating?
• Accelerating (speeding up) when the magnitude
  of the velocity is increasing
• Decelerating (slowing down) when the magnitude
  of the velocity is decreasing

40
Which pair of graphs shows the same motion?
41
Stage 1 The car moves forwards from the origin
to in the first 5 s.
42
Stage 2 The car moves backwards, passes the
origin, to in the next 5 s.
43
Stage 3 The car remains at rest in the last 5 s.

44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
What is the velocity for each stage of the
journey? b. What is the average (mean) velocity
for the whole journey
52
(No Transcript)
53
(No Transcript)
54
Distance or Displacement

• Distancehow far an object has traveled
• Indianapolis is about 45 miles away
• The distance to Indianapolis is 45 miles the
  distance back to Bloomington is 45 milesthe
  total distance traveled round trip is 90 miles
• Displacementhow far an object is from its
  original position (direction matters)
• The displacement to Indianapolis is 45 miles
  north the displacement back to Bloomington is 45
  miles souththe total displacement is 0 miles
• You can find displacement by
• Finding the area under a velocity time graph
• Using the equation d vavg t

55
(No Transcript)
56
(No Transcript)
57
Understanding the Connection Between Slope and
Velocity
The slope of a line for a distance vs. time graph
represents the velocity for the object in motion.
Slope can be determined using the following
formula
The change in y values divided by the change in x
values determines the average velocity for the
object between any two points.
58

• Pick two points on the line and determine their
  coordinates.
• Determine the difference in y-coordinates of
  these two points (rise).
• Determine the difference in x-coordinates for
  these two points (run).
• Divide the difference in y-coordinates by the
  difference in x-coordinates (rise/run or slope).

59
rise over run
Calculate the velocity between 3 and 4 seconds.
Note This is a constant speed graph, so the
velocity should be the same at all points.
60
(No Transcript)