PT3 KSSM Mathematics Form 2 (Speed And Acceleration) Chapter 9 Complete Revision
Summary
TLDRIn this educational video, Teacher Daisy teaches Form 2 Mathematics, focusing on Chapter 9: Speed and Acceleration. She explains the concepts of speed as a rate of distance over time, using examples like Aida's walk and sprinters' races to illustrate calculations. Daisy differentiates between uniform and non-uniform speed, provides examples, and explains acceleration as the rate of speed change. She covers average speed, acceleration units, and conversions between km/h and m/s. The video concludes with a practical example of calculating acceleration differences for a trip to a cultural festival.
Takeaways
- đ **Speed Calculation**: Speed is calculated as distance over time, e.g., Aida's speed is 20 meters per minute.
- đ **Sprinter's Speed**: Hyrule's speed is 9.82 meters per second, and Badrill's speed is 9.76 meters per second in a 100-meter sprint.
- đ **Uniform vs. Non-uniform Speed**: Uniform speed covers equal distances in equal time intervals, while non-uniform speed covers unequal distances.
- đ **Gradient and Speed**: Fari's driving speed is non-uniform as the distances covered in different time intervals are not equal.
- đïž **Uniform Speed in Golf**: The golf ball has a uniform speed as it covers equal distances in equal time intervals.
- đŽ **Average Speed**: Average speed is the total distance over the total time, e.g., Amir's average speed is 10.77 kilometers per hour.
- â±ïž **Acceleration**: Acceleration is the increase in speed over time, e.g., a bike race example shows an acceleration of 3 meters per second per second.
- đ **Car Acceleration**: A racing car's acceleration can be calculated by the change in speed over time, resulting in 0.0056 kilometers per second squared.
- đ **Motorcycle Acceleration**: A motorcycle's acceleration is 4 meters per second squared when it reaches 20 meters per second in 5 seconds.
- đ **Deceleration**: Deceleration is the decrease in speed, shown as negative acceleration, e.g., -5 meters per second squared for a motorcycle stopping.
- đ **Unit Conversion**: Conversion between kilometers per hour and meters per second involves understanding the relationship between these units.
Q & A
What is the formula for calculating speed?
-Speed is calculated as distance divided by time. The formula is: Speed = Distance / Time.
In the example of Aida walking 100 meters in 5 minutes, how is her speed calculated?
-Aida's speed is calculated by dividing the distance she walked (100 meters) by the time taken (5 minutes). So, Speed = 100 meters / 5 minutes = 20 meters per minute.
What is the difference between uniform and non-uniform speed?
-Uniform speed means covering equal distances in equal intervals of time, while non-uniform speed means covering unequal distances in equal intervals of time.
In the example of Fari driving a trailer, why is the speed considered non-uniform?
-Fari's speed is non-uniform because he covered different distances in different time intervals. For the first 2 hours, he traveled at 85 km/h, but for the next 4 hours, his speed decreased to 47.5 km/h.
How is average speed calculated?
-Average speed is calculated by dividing the total distance traveled by the total time taken. The formula is: Average Speed = Total Distance / Total Time.
What is acceleration, and how is it different from speed?
-Acceleration is the rate at which an objectâs speed changes over time, while speed is the distance covered per unit of time. Acceleration can be positive (increase in speed) or negative (deceleration or decrease in speed).
How is acceleration calculated in the example of a racing car reaching 120 km/h in 6 seconds?
-First, convert 120 km/h to km/s, which equals 0.033 km/s. Then, use the formula for acceleration: Acceleration = Change in Speed / Time = 0.033 km/s / 6 seconds = 0.0056 km/sÂČ.
What is the formula for converting speed from kilometers per hour to meters per second?
-To convert kilometers per hour to meters per second, multiply the speed by 5/18. The formula is: Speed (m/s) = Speed (km/h) * 5/18.
How is deceleration calculated when a motorcycle slows down from 20 m/s to 0 in 4 seconds?
-Deceleration is calculated using the formula: Deceleration = (Final Speed - Initial Speed) / Time. In this case, Deceleration = (0 - 20 m/s) / 4 seconds = -5 m/sÂČ. The negative sign indicates deceleration.
What is the difference in acceleration between Ronnieâs trips to and from the cultural festival?
-Ronnieâs acceleration when going to the festival is 24 km/hÂČ, while during the return trip, it is 40 km/hÂČ. The difference in acceleration is 16 km/hÂČ.
Outlines
đ Introduction to Speed and Acceleration
Teacher Daisy introduces chapter 9 of the Form 2 mathematics curriculum, focusing on speed and acceleration. She explains that speed is the rate of distance over time, using examples such as Aida walking 100 meters in five minutes at a speed of 20 meters per minute. She also discusses the speeds of sprinters Hyrule and Badrill, calculating their speeds during a 100-meter event. The paragraph further explains the concepts of uniform and non-uniform speed, using Margola and Marble B as examples. It concludes with examples of calculating average speed, such as Amir's cycling journey with a stop, and the uniform speed of a golf ball traveling between poles.
đïž Calculating Acceleration and Deceleration
This section delves into acceleration, defined as the increase in speed over time, and deceleration, which is the decrease in speed. Examples include a bike race where the speed increases from 10 to 16 meters per second, and a racing car accelerating from rest to 120 km/h in six seconds. The paragraph also covers the uniform acceleration of a motorcycle reaching 20 m/s in five seconds and its subsequent deceleration when brakes are applied. Unit conversion for speed and acceleration is discussed, including converting km/h to m/s and vice versa. The paragraph concludes with a problem-solving example involving Ronnie's cycling trip to a cultural festival, where the acceleration and time differences for the trip there and back are calculated.
đ Concept Map and Conclusion
The final paragraph summarizes the concept map for Form 2 Chapter 9 mathematics, which includes the topics of speed, acceleration, and their calculations. It encourages viewers to like, share, and subscribe to the channel for more educational content and invites them to comment with any questions they might have. The video concludes with a thank you note for watching.
Mindmap
Keywords
đĄSpeed
đĄAcceleration
đĄUniform Speed
đĄNon-Uniform Speed
đĄDeceleration
đĄAverage Speed
đĄDistance
đĄTime
đĄRate
đĄUnit Conversion
đĄContext
Highlights
Introduction to Chapter 9: Speed and Acceleration
Definition of Speed as a rate of distance over time
Example calculation of Aida's walking speed
Calculating the speed of sprinters Hyrule and Badrill
Explanation of uniform and non-uniform speed
Examples of uniform and non-uniform motion with Margola and Marble B
Determining non-uniform speed with Fari's driving example
Uniform speed of a golf ball in different segments of its trajectory
Definition and calculation of average speed
Example of calculating Amir's average cycling speed
Introduction to the concept of acceleration
Calculating acceleration during a bike race
Example of a racing car's acceleration from rest
Calculating the acceleration of a uniformly moving motorcycle
Determining the deceleration of a motorcycle after braking
Unit conversion of acceleration from km/h to m/s
Conversion of speed units from m/s to km/h
Example of converting acceleration from m/sÂČ to km/minÂČ
Calculating the difference in acceleration for a trip to and from a cultural festival
Concept map for Form 2 Chapter 9 Mathematics
Encouragement to like, share, and subscribe for more educational content
Transcripts
hi i am teacher daisy
now let's learn form 2 mathematics
chapter 9 speed and acceleration
in this chapter you will learn 9.1 speed
and 9.2 acceleration
9.1 speed
speed is a rate
speed is measured as distance moved over
time
example
aida walks to a shop over a distance of
100 meters in five minutes
calculate the speed
solution
speed equals distance over time equals
100 meters over five minutes
equals 20 meters per minute aida walks
20 meters every minute
example
hyrule and badrill are young sprinters
during a 100 meters event cairo finished
in 10.18 seconds while battle finished
in 10.25 seconds
calculate their speed respectively
solution speed of chi rule
equals 100 meters over 10.18 seconds
equals 9.82 meters per second
speed of bad roll
equals 100 meters over 10.25 seconds
equals 9.76 meters per second
uniform and non-uniform speed uniform
speed is the speed that covers equal
distance in equal interval of time
non-uniform speed is the speed that
covers unequal distance in equal
interval of time
margola moves at equal distance in equal
interval of time
so margula moves at a uniform speed
marble b moves at an equal distance in
equal interval of time so marbley moves
at a non-uniform speed
the gradient indicates the speed
example
fari drove a trailer for 170 kilometers
within the first two hours and 190
kilometers within the next four hours
did furry drive the trailer at a uniform
speed
explain
[Music]
solution speed for the first two hours
equals 170 kilometers over two hours
equals 85 kilometers per hour speed for
next four hours equals 190 kilometers
over 4 hours equals
47.5 kilometers per hour
therefore the speed of the trailer is
non-uniform
example
and sigma hesh hit the golf ball from
pole p to pole s
passing through pole q and polar
did the golf ball have a uniform speed
explain
[Music]
solution
speed of ball from p to q equals 40
meters over two seconds
equals 20 meters per second
speed of ball from r to s equals 60
meters over three seconds
equals 20 meters per second
speed of ball from kudo r equals 70
meters over 3.5 seconds equals 20 meters
per second
therefore the speed of the golf ball is
uniform
average speed average speed equals total
distance over total time
example
amir started cycling from his house
satanic at 9 00 am
along the way he stopped at a pizzeria
to rest and eat before he resumed his
journey
he arrived to town at 12 15 p.m
calculate the average speed of the
journey in kilometer per hour
solution total distance equals 10
kilometers plus 25 kilometers
equals 35 kilometers
total time taken equals 12 colon 15
minus 9 o'clock
equals 3 hours 15 minutes
average speed
equals 35 kilometers over 3.25 hours
equals
10.77 kilometers per hour
9.2 acceleration acceleration is the
increase in speed
deceleration is the decrease in speed
for instance you are taking a bike race
and goes a steady 10 meters per second
now you start cycling faster
you increase to 16 meters per second
over the next two seconds
acceleration equals change in speed over
time
equals 16 minus 10 meter per second over
two seconds equals six meters per second
over two seconds
equals three meters per second per
second your speed changes by 3 meters
per second per second
example
a racing car accelerates from a
stationary state and reaches a speed of
120 kilometers per hour in six seconds
calculate the acceleration
change of speed
equals 120 kilometers per hour minus
zero kilometers per hour
equals 120 kilometers per hour
120 kilometers per hour equals 120
kilometers over 60 minutes times 60
seconds
equals
0.033 kilometers per second
acceleration equals
0.033 kilometers per second over 6
seconds
equals
0.0056 kilometers per second per second
or km over second squared
example
a motorcycle moves from a stationary
state and accelerates uniformly to reach
a speed of 20 meters per second in 5
seconds
what is the acceleration of the
motorcycle
solution acceleration equals 20 minus 0
meter per second over 5 seconds equals
20 meters per second over 5 seconds
equals 4 meters over second squared
after the motorcyclist applies the brake
the motorcycle moves slower at a uniform
rate
until it stops within 4 seconds
what is the change in speed of the
motorcycle
solution acceleration equals
0-20 meter per second over four seconds
equals negative 20 meters per second
over four seconds
equals negative five meters over second
squared
thus the deceleration is five meters
over second squared
unit conversion acceleration equals
speed over time
kilometer per hour over hour
equals km over hour squared or km hour
to the power of negative 2 or kilometer
per hour per hour
acceleration equals speed over time
meter per second over second
equals m over second squared or meter
second to the power of negative two or
meter per second per second
how to convert kilometer per hour into
meter per second
kilometer per hour
equals one kilometer over one hour
equals one times one thousand meters
over sixty times sixty seconds
equals one thousand meters over three
thousand six hundred seconds
equals five meters over 18 seconds
how to convert meter per second a
kilometer per hour
meter per second
equals one meter over one second
equals one one thousandth of a kilometer
over 160 times 60 hour equals 60 times
60 kilometers over 1000 hours
equals 18 over 5 kilometers per hour
example
convert 420 meters per minute per minute
to km per minute per minute
solution
420 meters per minute over minute equals
420 meters per minute divide by minute
equals 420 times 1 meter over minute
divide by minute
meter change to kilometer
equals 420 times 1 1000 of a kilometer
over minute divide by minute
equals 421 thousandths of a kilometer
over minute divide by minute
equals 0.42 kilometers over minute times
one over minute
equals zero point four two kilometers
over minutes squared
example
ronnie cycles for three quarters of an
hour from her house
to the cultural festival held in the
city
with a speed change of 18 kilometers per
hour
traveling to the cultural festival takes
40 percent less time
compared to the time of the return trip
at the same speed change
calculate the difference in acceleration
between the trips to and from the
cultural festival
solution acceleration when going equals
18 kilometers over hour over three
quarters hour
equals 24 kilometers over hour squared
time reduced
equals 40 over 100 times three quarters
hour equals 0.3 hour
time taken for return trip equals 0.75
hour minus 0.3 hour
equals 0.45 hour
acceleration during return trip equals
18 kilometers over hour over 0.45 hour
equals 40 kilometers per hour squared
difference in acceleration equals 40
kilometers over hour squared minus 24
kilometers over r squared
equals 16 kilometers over hour squared
the concept map for form 2 chapter 9
mathematics is as below
if you find this video helpful don't
forget to like share and subscribe our
channel and if you got any question can
comment below thanks for watching
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