Analysis and Approaches for IBDP Maths Ebook 2 | Page 226
Your Practice Set – Analysis and Approaches for IBDP Mathematics
(c)
The total distance travelled
�
8
0
� � v( t) dt
(M1) for valid approach
�
8
� � �
� � �ln cos �3t�
dt
0
� �
� 6 �
(A1) for substitution
� 0.0245095082 m
� 0.0245 m
A1
� � �
(d) v� �ln cos ��3t�
�
� 6 �
[3]
1
v � ln
� � �
cos��3t
� �
� 6 �
� � �
v� ln sec��3t�
�
� 6 �
1 � ln sec
2 � � ��
v� � �� 3 t�
��
2 � � 6��
�
v� � �� � ��
2 � � 6�
1 ln tan 2 � � � 3 t 1
2
1 ��a
� �
�v
� ln � 1
2 ��
�
�3�
�
� �
�
v � �
2 � 9
2
1 a ln � 1
�
�
�
2
1 �a
� 9�
v � ln � �
2 � 9 �
�
�
�
M1
A1
A1
A1
AG
[4]
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