Analysis and Approaches for IBDP Maths Ebook 2 | Page 199

200t
at () ��
(25 � t )
2 2
� 100 �
(c) s( t) � � � �2 dt
2 �
�25
� t �
(M1) for valid approach
(d)
� 100 �
s( t) ��
� �2 dt
2 2 �
�5
� t �
100 t
s( t) arctan � �
� � �� 2t � C
5 �5�
t
s( t) 20arctan � �
� � �� 2t � C
�5
�
The total distance travelled
7
� � v( t) dt
(M1) for valid approach
�
0
100
25 � t
AG
7
� �2dt
(A1) for substitution
0 2
� 6.404990371 m
A1
� 6.40 m
A1
(e) vt ( ) � 0 and at ( ) � 0
t � 5 and t � 0
R2
�5 � t � 10
A1
200t
(f) at () ��
2 2
(25 � t )
dv
200t
��
d t (25 � t )
2 2
d v d 200
�
s � �
t
ds d t (25 � t )
2 2
dv
� 100 � 200t
��
� 2�� �
ds �25 �t � (25 �t
)
2 2 2
dv
200t
� 100
� � �
d s (25 �t ) �25
�t
t�10
2 2 2
�
� 2�
�
dv
200(10) � 100
� � �
d s (25 �10 ) �25 �10
dv
16 � 5 �
� � � � �
ds �
25 � 6 �
t
5
dv
8 s
ds
15
t�5
�1
2 2 2
�
� 2�
�
�1
A1
M1
A1
M1
�1
� AG
[3]
[2]
[3]
[3]
[4]
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