Analysis and Approaches for IBDP Maths Ebook 2 | Page 227

Exercise 70
1
2�
1. A particle moves in a straight line with velocity v ms
� . At time t s , 0 �t
� , the
3
dv
2
velocity is given by the differential equation 4 v
dt � � . The initial velocity is 1
2 ms � .
(a) Find v in terms of t .
(b)
Let
Hence, find the distance travelled in
2�
0 �t
� .
3
s m be the displacement of the particle. When
(c) Find s in terms of t .
(d) Show that v � �s( s � 4) .
2. A particle moves in a straight line with acceleration
displacement
�
t � , s � 0 .
2
2
a ms � , velocity
v ms
�1
and
s m . At time t s , the acceleration is given by the differential equation
v �150
a � . The initial velocity and the initial displacement are
300
respectively.
1
0 ms � and 0m
[7]
[3]
[5]
[5]
15
(a) Find v in terms of t .
(b) Hence, find t when v � 5 .
(c)
Show that
� 150 �
s�
� �300 � �dv
� v �150
�
.
(d) Hence, find s when v � 5 .
[7]
[3]
[5]
[5]
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