Analysis and Approaches for IBDP Maths Ebook 1 | Page 214

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. A particle moves in a straight line. Its initial displacement is one metre. Its velocity,
1
v ms �
, at time t seconds, is given by
v� �cos�t, for 0�t
� 5.
(a)
Find the expression of s , the displacement of the particle.
(b) Find the values of t for which the displacement of the particle is 0 m.
(c)
Find all possible values of t for which the acceleration is positive.
It is given that there are five stationary points of the graph of s , for 0�t
� 5.
[5]
[4]
[6]
(d)
Write down the number of times for which the particle is at rest.
[1]
4. A particle moves in a straight line. Its initial displacement is zero metres and its initial
1
velocity is 48 ms � 2
. Its acceleration, a ms � , at time t seconds, is given by
(a)
(b)
a � t � t � t � , for 0�t
� 5.
2
( 2)(4 25 38)
Show that the displacement of the particle is given by
1 5 11 4 44 3 2
s � t � t � t �38t � 48t
.
5 4 3
Find all possible values of t for which the displacement and acceleration are both
negative.
The table below shows the information of the graph of v , for 0�t
� 5.
t 0�t
� 2 t � 2 2�t
� 3 t � 3 3�t
� 4 t � 4 4�t
� 5
v positive 0 positive 0 negative 0 positive
(c) (i) Write down the number of times for which the particle is at rest.
[8]
[4]
(ii)
Write down the number of times for which the particle changes its
direction.
[3]
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