# acceleration

```MOTION
• We now know that unbalanced
forces can change motion
LET’S RACE!
JOBS:
3 measurers to make track
4 timers &amp; 4 recorders at 5 meter mark
4 timers &amp; 4 recorders at 10 meter mark
4 timers &amp; 4 recorders at 15 meter mark
1 Hopper
1 Backward walker
1 regular walker
1 Speed walker
Let’s Race!
NOW WE ARE GOING TO LOOK AT
WAYS TO DESCRIBE AND
MEASURE MOTION
SPEED
HOW DO WE DESCRIBE SPEED?
HOW FAST SOMETHING GOES
How do we CALCULATE SPEED?
• How we describe the speed of a CAR:
– Miles per hour (MPH)
OR
– Kilometers per hour (km/h)
• What does the miles or kilometers measure?
– They are units for distance
• What does the hour measure?
– It is a unit for time
• What does the “per” or “/” mean in math?
– division
SPEED =RATE that an
object moves
Distance (D)
Rate (speed)=
Time (T)
Units: Meters/ sec (m/sec)
STEPS IN PROBLEM
SOLVING
 STEP 1. Write the formula
 STEP 2. Substitute given
numbers and units
 STEP 3. Solve for the
unknown.
SAMPLE PROBLEM:
At what speed did a plane
fly if it traveled 1760
meters in 8 seconds?
SOLUTION
speed” so use:
Rate (Speed) = Distance/Time
SOLUTION
Step 1.
Speed = Distance/Time
SOLUTION
Step 2. substitute distance = 1760 meters
substitute time = 8 seconds
Speed = 1760 meters/ 8 seconds
SOLUTION
Step 1.
Speed = Distance/Time
Step 2.
Speed = 1760 meters/ 8sec
SOLUTION
Speed = 1760m / 8 sec = 220 m/sec
SOLUTION
Step 1.
Speed = Distance/Time
Step 2.
Speed = 1760 m/ 8 sec
Step 3.
Speed = 220 m/sec
VELOCITY
AND
ACCELERATION
VELOCITY
SPEED IN A GIVEN
DIRECTION
D
V
EX) 88 km / hr
southwest
=
T
AND
direction
A bird flies south at
20 m/s.
• SPEED = 20 m/s
• VELOCITY = 20 m/s south
CONSTANT VELOCITY
-SAME SPEED
AND
-SAME DIRECTION
ACCELERATION
 happens when VELOCITY IS CHANGING
 change in Speed and/or Direction
Units = meters per sec per sec
SPEEDING UP
SLOWING DOWN
CHANGING DIRECTION
CHANGING VELOCITY=
ACCELERATION
NEED AT LEAST 1 THING DIFFERENT
SPEED
DIRECTION
DIFFERENT
DIFFERENT
SAME
DIFFERENT
DIFFERENT
SAME
Speeding up = POSITIVE ACCELERATION
0
Slowing down = NEGATIVE ACCELERATION
A.K.A. DECELERATION
DECELERATION
• decrease in velocity
• negative acceleration
• slows down
CIRCULAR MOTION
 Why is object is
accelerating even with
constant speed?
 because direction is
changing
 Does it have constant
velocity?
 No
ACCELERATION
Rate of change in
velocity
A=
Final velocity – Original Velocity
Time
Change in velocity divided by the time
during which this change occurs
Acceleration =
Time =
VF - VI
Acceleration
VF - VI
t
A roller coaster’s velocity at
the top of the hill is 10 m/s.
Two seconds later it reaches
the bottom of the hill with a
velocity of 26 m/s. What is
the acceleration of
the roller coaster?
SOLUTION:
A=
A=
Final Velocity – Original Velocity
Time
26 m/s- 10 m/s
2s
A=
16 m/s
2s
A= 8 m/sec/sec
Velocity vs Time - Acceleration
Distance vs Time - Acceleration
500
Velocity (m/s)
Distance (meters)
600
400
300
200
100
0
0
1
2
3
4
5
6
7
8
9
180
160
140
120
100
80
60
40
20
0
0
10
1
2
3
4
600
600
500
500
400
300
200
0
5
6
10
200
0
4
9
300
100
3
8
400
100
2
7
Velocity vs Time - Negative Acceleration
Velocity (m/s)
Disatnce (meters)
Distance vs Time - Negative Acceleration
1
6
Time (min)
Time (seconds)
0
5
7
8
9
0
1
2
3
4
5
6
Time (min)
Time (min)
MOTION GRAPHS
7
8
9
10
Velocity vs Time - Constant Speed
80
70
60
50
40
30
20
10
0
Velocity (m/s)
Distance (m)
Distance vs Time - Constant Speed
0
1
2
3
Time (min)
4
5
16
14
12
10
8
6
4
2
0
0
1
2
3
4
5
Time (min)
6
7
8
9
10
A car accelerated
from 0 m/sec to 30
m/sec in 10 sec. What
was the rate of
acceleration?
3 m/sec/sec
A roller coaster is moving at 25
m/sec at the bottom of a hill.
Three sec. later it reaches the
top of the next hill, moving at
10 m/sec. What is the
deceleration of the roller
coaster?
- 5 m/sec/sec
A train accelerated
from 5 km/hr to 55
km/hr in 0.5 hr. What
was the rate of
acceleration?
100 km/hr/hr
Definitions:
A change in position in a certain amount of time is __________.
__________________ is the rate at which an object moves and
is determined by dividing ____________ by _____________.
_________________________ is speed that does not change.
_________________________ is calculated by dividing the
total distance by the total time.
CONSTANT SPEED
SPEED
THAT
DOES NOT
CHANGE
CONSTANT SPEED
Distance (km)
Michelle Goes on a Bike Ride
5.Describe the motion shown in the
graph
80
70
60
50
40
30
20
10
0
6.How many different rates are shown?
Label them using A, B, . . . . .
1
2
3
4
5
6
Time (hours)
7. Calculate the speeds for the different segments of the journey (Hint - you will have to use change in distance!)
Time
(hours)
A
B
C
D
Distance
(km)
Speed
(min/km)
8. What is the average speed for the entire trip? How does the value compare
9. Can you predict how far Michelle will travel if she travels for another 2
hours? Why or why not? What additional information do you need?
Distance (km)
Michelle Goes on a Bike Ride
5.Describe the motion shown in the
graph (moving at varying speed)
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
6.How many different rates are shown?
Label them using A, B, . . . . .
4 different rates
3 if you notice A and D are same
Time (hours)
7. Calculate the speeds for the different segments of the journey (Hint - you will have to use change in distance!)
Time (hours)
A (1 h)
B (1h)
C (2 h)
D (1h)
Distance (km)
10
0
40
10
Speed (km/h)
10
0
20
10
8. What is the average speed for the entire trip? How does the value compare
to your calculations above? 11.7 (from graph) or 12 km/h (from math)
9. Can you predict how far Michelle will travel if she travels for another 2 hours?
Why or why not? What additional information do you need?
no, not constant rate but can get estimate using average speed; need more rates
1. A runner moving eastward covers a
distance of a 100 meters in 10 seconds.
What is his velocity?
Given: D= 100 m
1.Formula
2.Work
T= 10s dir= East
V= d/t with dir
V= 100m/10s East
V= 10m/s East
2. A tropical disturbance spotted east of the
Philippines was moving at 60 km per hour at
a Northwesterly direction and having
maximum sustained winds of 150 km/h?
What is the storm’s velocity?
Given: S= 60km/h dir= NW
V= 60km/h NW
3. Seve is walking to a friend’s house. He walks 500m for 10
minutes, then realizes he forgot something important to
bring. He turns around, and hurries back to his house. The
walk/jog back takes him 5 minutes.
Given: Total D= 500m + 500m = 1,000m
Total T= 10min + 5 min= 15min x 60 sec/min
= 900 sec
T= 10 min
D= 500m
D= 500m
T= 5 min
3. Seve is walking to a friend’s house. He walks 500m for 10
minutes, then realizes he forgot something important to
bring. He turns around, and hurries back to his house. The
walk/jog back takes him 5 minutes.
a. What was his average speed in m/sec?
Given: Total D= 500m + 500m = 1,000m
Total T= 10min + 5 min= 15min x 60 sec/min
= 900 sec (15 min)
1.Formula Ave S = total D/total T
2.Work
Ave S = 1,000m/900s
3.Answer Ave S = 1.1 m/s
3. Seve is walking to a friend’s house. He walks 500m for 10
minutes, then realizes he forgot something important to
bring. He turns around, and hurries back to his house. The
walk/jog back takes him 5 minutes.
b. What was Seve’s velocity (in m/s) while walking to his
friend’s house?
Given: D= 500m T= 10min x 60 sec/min= 600 sec
dir = forward (to his friend’s house)
1.Formula
V= d/t with dir
2. Work
V= 500m/600s to friend’s house
V= 0.83 m/s to friend’s house
4. Sean is running around the track oval. The oval is 800m
long. He is running at a constant speed. It takes him 180 s
to complete the track and get back to where he started.
a. What is Sean’s speed in m/s?
Given: d= 800 m
t= 180 s
running at constant speed
a. What is Sean’s speed in m/s?
Given: d= 800 m
t= 180 s running at constant speed
1. Formula S= d/t
2. Work
S= 800m/180s around oval