Analysis and Approaches for IBDP Maths Ebook 2 | Page 163

Exercise 49
1. A particle moves along a straight line such that after t seconds its displacement s , in
2 4
metres, satisfies the equation s � 4s �5t
� 0. Find the expressions for its velocity and
its acceleration, giving the answers in terms of s and t .
[6]
11
2. A particle moves along a straight line such that after t seconds its displacement s , in
2
metres, satisfies the equation s� arctan t . Find the acceleration of the particle after 2
seconds.
[5]
3. A particle moves along a straight line such that after t seconds its displacement s , in
metres, satisfies the equation s�log 4(3� 2 e
t ) . Show that the acceleration of the particle
after ln 2 seconds is
12 ms
ln 4
�2
� .
[5]
4. A particle moves along a straight line such that after t seconds its displacement s , in
metres, satisfies the equation s � t arccos t , 0�t
� 1.
(a)
(b)
Find the value of t when the particle is at rest.
2
t � k
The acceleration of the particle is given by a �
(1 � t )
k .
3
2 2
[3]
, k � . Find the value of
[3]
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