Analysis and Approaches for IBDP Maths Ebook 1 | Seite 213

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(e) vt ( ) � 0 and at ( ) � 0
t � 3 and t � 3
R2
�t
� 3
A2 N2
[4]
Exercise 71
1. A particle moves in a straight line. Its velocity,
v ms
� 1
, at time t seconds, is given by
v
3
� � � , for 0 8
( t 4)
�t
� .
(a)
(b)
(c)
(d)
(e)
Find the initial velocity.
Find the value of t for which the velocity of the particle is
� 27 ms �1 .
Find the total distance the particle travels during the first seven seconds.
Show that the acceleration of the particle is given by
a
2
� � � .
3( t 4)
Find all possible values of t for which the velocity and acceleration are both
negative.
[2]
[3]
[3]
[3]
[4]
16
2. A particle moves in a straight line. Its initial displacement is zero metres. Its velocity,
1
v ms �
, at time t seconds, is given by
v t t t
�t
� .
3 2
� �2 �12 � 24 � 16 , for 0 4
(a) Find the expression of s , the displacement of the particle.
[4]
(b) Find the exact value of the displacement of the particle at t � 3.3 .
[2]
(c) Find the total distance the particle travels during the first 3.3 seconds.
[3]
2
(d) Show that the acceleration of the particle is given by a� �6( t� 2) .
[4]
(e) Find all possible values of t for which the velocity is positive and the acceleration
is negative.
[4]
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