Miscellaneous Exercise 21

Dr Lee Chu Keong (http://ascklee.org/)

0

Solutions to Miscellaneous Exercise 21 (Ho Soo Thong & Khor Nyak Hiong’s Panpac Additional Mathematics)

Solved by: Dr Lee Chu Keong ([email protected])

Dr Lee Chu Keong (http://ascklee.org/)

1

Miscellaneous Exercise 21 Question 1(a)

( )

( )( )

The particle is instantaneously at rest at .

( )

Question 1(b)

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(√ )(√ )

√

The particle is next at O at √ :

(√ )

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Question 1(c)

( ) ( )

( ) ( )

Question 1(d)

Summary:

,

Dr Lee Chu Keong (http://ascklee.org/)

2

,

,

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Question 2(a)

When ,

When :

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Question 2(b)

( )( )

( ) ( )

( )

Question 3(a)

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( ( ) )

Dr Lee Chu Keong (http://ascklee.org/)

3

Question 3(b)

( )

( )

( )

( )

Question 3(c)

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( )

( )

( )

( )

( )

( )( )

Dr Lee Chu Keong (http://ascklee.org/)

4

At , :

( ) ( )

(

)

Question 4(a)

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“a particle starts from rest” which means that at , :

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When :

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Question 4(b)

At , :

( ) ( )

( ) ( )

Question 5(a)

When :

Dr Lee Chu Keong (http://ascklee.org/)

5

( )

( )

Question 5(b)

When , :

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( )

Question 6(a)

( )( )

At , the particle comes to instantaneous rest at A

At , the particle comes to instantaneous rest at B

“t seconds after passing though O” means that at , :

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( ) ( )

Question 6(b)

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( ) ( )

Dr Lee Chu Keong (http://ascklee.org/)

6

( )

( ) ( )

Question 6(c)

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( ) ( )

Question 7

When , :

When , :

When , :

( ) ( )

Dr Lee Chu Keong (http://ascklee.org/)

7

At :

( )

√

At √ :

(√ )

(√ )

( √ ) √

√ √

√

Summary:

At ,

At √ , √

At ,

√ √ √ Question 8(a)

Dr Lee Chu Keong (http://ascklee.org/)

8

Question 8(b)

( )

When , :

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(

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Question 9(a)

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( )

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Question 9(b)

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Dr Lee Chu Keong (http://ascklee.org/)

9

Question 9(c)

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Question 9(d)

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( )

( )

when

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Question 10(a) ( )

Question 10(b)

At :

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When , :

( ) ( )

When :

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Question 10(c)

Dr Lee Chu Keong (http://ascklee.org/)

10

The plot of below shows that the particle will never return to O.

Question 11(a)

At :

Question 11(b)

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1 2 3 4t

10

20

30

40

50

s

Dr Lee Chu Keong (http://ascklee.org/)

11

( )

( )

Question 11(c)

(

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