Analysis and Approaches for IBDP Maths Ebook 2 | Page 162

Your Practice Set – Analysis and Approaches for IBDP Mathematics
49
Paper 2 Section A – Problems in Kinematics
Example
A particle moves along a straight line such that after t seconds its displacement s , in
2 2
metres, satisfies the equation s � 2s � 4t
� 0 . Find the expressions for its velocity and
its acceleration, giving the answers in terms of s and t .
[6]
Solution
2 2
s � 2s � 4t
� 0
d 2 d d 2 d
( s ) � (2 s) � (4 t ) � (0)
(M1) for valid approach
dt dt dt dt
ds
ds
2s
� 2 �8t
� 0
(A1) for correct approach
dt
dt
ds
(2s� 2) � � 8t
dt
ds
8t
��
dt
2s�
2
ds
4t
�� A1
dt
s � 1
d d
2 ( s �1) (4 t) � (4 t) ( s �1)
d s
�� dt dt
(A1) for correct approach
2 2
d t
( s�1)
ds
2 ( s�1)(4) �4t
d s
��
dt
2 2
d t ( s�1)
2
d s 4 4t 4t
� � � �
2 2 � �
dt s �1 ( s �1) s �1
2 2
d s 4 16t
� � �
dt s �1 ( s �1)
2 3
�
�
�
�
(M1) for substitution
A1
[6]
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