Analysis and Approaches for IBDP Maths Ebook 2 | Page 201

3. A particle moves in a straight line. Its initial displacement is one metre. Its velocity,
v ms
� 1
, at time t seconds, is given by
� 1
� � t 0 � t � 1
10 ��
1 2 1
v( t) � � t � t 1� t � 3 .
�� 10 5
0 otherwise
� �
13
(a) Find the expression of st (), the displacement of the particle.
(b) Find the values of t for which the displacement of the particle is 1 m.
(c)
Find all possible values of t for which the acceleration is less than
(d) Show that d t
�
5
dv
10v
�1
for 1�t
� 3.
3 ms
10
� 2
.
[7]
[3]
[4]
[4]
4. A particle moves in a straight line. Its initial displacement is 5000 m and its initial
19ln 3
1
velocity is 0 ms � 2
. Its acceleration, a ms � , at time t seconds, is given by
at ( ) 38ln3 3
�t
� .
�0.38t
� � , for 0 10
(a) Show that the displacement of the particle is given by
5000 �0.38t
s( t) � (3 � (0.38ln3) t)
.
19ln3
(b) Find the value of t for which s�( t) � a( t)
.
(c) Find the total distance the particle travels in the last four seconds.
(d) Show that d t
�
50 .
dv
19 ln 3(100 � v)
[9]
[3]
[3]
[3]
www.seprodstore.com
191