Analysis and Approaches for IBDP Maths Ebook 2 | Page 224

Your Practice Set – Analysis and Approaches for IBDP Mathematics
70
Paper 2 Section B – Problems in Kinematics
Example
A particle moves in a straight line with acceleration
a ms
�2
and velocity
v ms
� 1
. At time
�
da
2
t s , 0 �t
� , the acceleration is given by the differential equation a 9 0
6
dt � � � . The
initial acceleration and the initial velocity are
(a) Find a in terms of t .
(b) Find v in terms of t .
2
3 ms � and
�
(c) Hence, find the distance travelled in 0 �t
� .
8
(d)
Show that
3
2
�1
� ln ms respectively.
2
1 �a
� 9�
v � ln � �
2 � 9 � . [4]
[7]
[7]
[3]
Solution
(a)
da
a
2
9 0
dt � � �
da
2
( a 9)
dt � � �
1
d d
2
9 a ��
a �
t
(M1) for valid approach
1
d d
2
9 a ��
a �
t
1
� da��
dt
2 2
a � 3
�
1 a arctan � �t� C
A1
3 3
a
arctan � �3t�
C
3
a
� tan( �3 t�
C)
3
� � (A1) for correct approach
214
SE Production Limited