Analysis and Approaches for IBDP Maths Ebook 2 | Page 228

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. A particle moves in a straight line with velocity
v ms
� 1
. At time s
t , 0 �t
� ln3, the
velocity is given by the differential equation d v v ( v �
��
3) . The initial velocity is
dt
3
1
1.5 ms � .
(a) (i) Express
1
xx� ( 3)
in partial fractions.
Let
(ii) Hence, find v in terms of t .
s m be the displacement of the particle. The initial displacement is � 2ln 4.5 m .
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(b) Show that s � ln 2( 3) 3
v �
.
[8]
2
4. A particle moves in a straight line with acceleration a ms � . At time t s , 0�t
� 2, the
acceleration is given by the differential equation
4
ms
2
e �1
�2
.
2
d � 4
a a a
� . The initial acceleration is
dt
4
1
(a) (i) Express
2
x � 4x
in partial fractions.
Let
(ii) Hence, find a in terms of t .
v m be the velocity of the particle. The initial velocity is
(b) Show that the particle never stops in 0�t
� 2.
(8 4ln(1 )) ms
2 1
� � e � � .
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