Analysis and Approaches for IBDP Maths Ebook 2 | Page 198

Your Practice Set – Analysis and Approaches for IBDP Mathematics
61
Paper 2 Section B – Problems in Kinematics
Example
A particle moves in a straight line. Its velocity,
v ms
� 1
, at time t seconds, is given by
100
vt ( ) � �2
, for 0 �t
� 10 .
2
25 � t
(a)
Find the value of t for which the particle is at rest.
200t
(b) Show that the acceleration of the particle is given by at () �� .
2 2
(25 � t )
(c) Find the expression of st (), the displacement of the particle.
(d)
(e)
(f)
Find the total distance the particle travels during the first seven seconds.
Find all possible values of t for which the velocity and acceleration are both
negative.
Show that
dv
8 s
ds
15
t�5
�1
� .
[3]
[3]
[2]
[3]
[3]
[4]
Solution
(a) vt ( ) � 0
(M1) for setting equation
100
25 � t
100
25 � t
2
2
�2�0
� 2
2
25 t 50
� � (A1) for correct approach
2
t � 25
t �� 5 (Rejected) or t � 5
A1
(b) a( t) � v�( t)
M1
� 1 �
a( t) ��100 � (2 t)
2 2�
�(25 � t ) �
A2
[3]
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