PT3 KSSM Mathematics Form 2 (Speed And Acceleration) Chapter 9 Complete Revision

Summary

In 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

• 📏 **Speed Calculation**: Speed is calculated as distance over time, e.g., Aida's speed is 20 meters per minute.
• 🏃 **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.
• 🔄 **Uniform vs. Non-uniform Speed**: Uniform speed covers equal distances in equal time intervals, while non-uniform speed covers unequal distances.
• 🚗 **Gradient and Speed**: Fari's driving speed is non-uniform as the distances covered in different time intervals are not equal.
• 🏌️ **Uniform Speed in Golf**: The golf ball has a uniform speed as it covers equal distances in equal time intervals.
• 🚴 **Average Speed**: Average speed is the total distance over the total time, e.g., Amir's average speed is 10.77 kilometers per hour.
• ⏱️ **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.
• 🚗 **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.
• 🏍 **Motorcycle Acceleration**: A motorcycle's acceleration is 4 meters per second squared when it reaches 20 meters per second in 5 seconds.
• 🛑 **Deceleration**: Deceleration is the decrease in speed, shown as negative acceleration, e.g., -5 meters per second squared for a motorcycle stopping.
• 🔄 **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 object’s 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/s².

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/s². The negative sign indicates deceleration.

What is the difference in acceleration between Ronnie’s trips to and from the cultural festival?

Ronnie’s acceleration when going to the festival is 24 km/h², while during the return trip, it is 40 km/h². The difference in acceleration is 16 km/h².

Outlines

00:00

📚 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.

05:02

🏎️ 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.

10:03

📊 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.

Keywords

💡Speed

Speed is defined as the rate at which an object covers distance over time. In the context of the video, it is a fundamental concept in physics and mathematics, used to describe how fast an object is moving. For instance, the script mentions Aida walking 100 meters in five minutes, which calculates to a speed of 20 meters per minute. This example illustrates how speed is calculated and its application in everyday scenarios.

💡Acceleration

Acceleration is the rate of change of speed with respect to time. It indicates how quickly an object's speed is increasing or decreasing. The video explains acceleration by showing how a racing car goes from a stationary state to a speed of 120 kilometers per hour in six seconds, which is calculated as an acceleration of 0.0056 kilometers per second squared.

💡Uniform Speed

Uniform speed refers to a situation where an object covers equal distances in equal intervals of time. This concept is used to describe consistent motion without any change in speed. The video uses the example of Margola moving at equal distances in equal intervals of time to illustrate uniform speed.

💡Non-Uniform Speed

Non-uniform speed is the opposite of uniform speed, where an object covers unequal distances in equal intervals of time. This concept is important for understanding variable motion. The video contrasts this with uniform speed by discussing how Marble B moves at unequal distances in equal intervals of time, thus moving at a non-uniform speed.

💡Deceleration

Deceleration is the negative acceleration, which means it is the decrease in speed. The video explains deceleration by describing a scenario where a motorcyclist applies the brake, causing the motorcycle to slow down uniformly until it stops, with a deceleration calculated as five meters per second squared.

💡Average Speed

Average speed is calculated as the total distance traveled divided by the total time taken. It provides a general idea of how fast an object has moved over a period, including any stops or changes in speed. The video gives an example of Amir cycling from his house to a town, stopping at a pizzeria, and then continuing to his destination, with the average speed calculated based on the total distance and time.

💡Distance

Distance is a measure of the total path traveled by an object, irrespective of the direction of motion. In the video, distance is used in calculations of speed and acceleration, such as when calculating Aida's speed over a distance of 100 meters or when determining the average speed based on the total distance traveled.

💡Time

Time is a crucial factor in calculating speed and acceleration, representing the duration over which motion occurs. The video emphasizes the importance of time in various calculations, such as determining Aida's speed over a period of five minutes or calculating the acceleration of a racing car over six seconds.

💡Rate

Rate, in the context of the video, refers to the measure of an occurrence per unit of time, such as speed, which is a rate of distance per time. The script uses the term to introduce the concept of speed as a rate, setting the stage for more complex discussions on acceleration and other related topics.

💡Unit Conversion

Unit conversion is the process of changing the units of measurement from one system to another. The video explains how to convert between kilometers per hour and meters per second, which is essential for understanding and comparing speeds and accelerations across different units.

💡Context

Context in the video refers to the specific situations or scenarios in which the concepts of speed, acceleration, and other related terms are applied. Examples include Aida walking to a shop, sprinters in a race, and a golf ball's motion, which all provide real-world contexts for understanding the mathematical and physical principles discussed.

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/s² to km/min²

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

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