Analysis and Approaches for IBDP Maths Ebook 2 | Page 200

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 61
1. A particle moves in a straight line. Its velocity,
v ms
� 1
, at time t seconds, is given by
v( t) (12 1.5 t)
�t
� .
3
� � , for 0 16
(a)
(b)
Find the initial velocity.
Find the value of t for which the velocity of the particle is
1
3.375 ms � .
(c) Find the exact total distance the particle travels during 7 �t
� 11.
(d)
Show that the acceleration of the particle is given by
(e) Find all possible values of t for which the v( t) � a( t)
.
(f)
Show that
dv
4.5
�� s
ds
12 �1.5t
�1
.
a( t) 4.5(12 1.5 t)
2
� � � .
[2]
[3]
[3]
[3]
[2]
[3]
2. A particle moves in a straight line. Its velocity,
v ms
� 1
, at time t seconds, is given by
v( t) � �1� ln 2 � cos t , for 0�t
� 1.
(a)
Find the value of t for which the velocity of the particle is
(b) Find all possible values of t for which the vt ( ) � 0.05 .
(c)
Find the total distance the particle travels in the first second.
1
0.01ms � .
(d) Let at () be the acceleration of the particle at time t seconds. Find the
(e)
acceleration at the time when the particle is at rest.
Find all possible values of t for which the
1
v( t) �a( t)
� .
2
[3]
[3]
[3]
[6]
[3]
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