Analysis and Approaches for IBDP Maths Ebook 1 | Page 180

Your Practice Set – Analysis and Approaches for IBDP Mathematics
60
Paper 2 Section A – Problems in kinematics
Example
The displacement, in centimetres, of a particle from an origin, O , at time t seconds, is
3 2
given by s( t) �t sin t � 3t cos t , 0 �t
� 2.5 .
(a) Write down the maximum distance of the particle from O .
(b)
Find the acceleration of the particle at the instant it first changes direction.
[2]
[5]
Solution
(a) 5.67 m A2 N2
[2]
(b) The particle first changes direction at 1.5707983 s. (M1)(A1) for valid approach
s�
() t
� � � � � (A1) for differentiation
2 3 2
(3 t )(sin t) ( t )(cos t) (6 t)(cos t) (3 t )( sin t)
3
�( t � 6 t)cos
t
The acceleration at 1.5707983 s
� s��(1.5707983)
(M1) for substitution
�� 13.30062
-2
�� 13.3 cms
A1 N2
[5]
Exercise 60
1. The displacement, in centimetres, of a particle from an origin, O , at time t seconds, is
3
given by s( t) � �t cos t � 6sin t , 0�t
� 4.
(a) Write down the maximum distance of the particle from O .
(b)
Find the acceleration of the particle at the instant it first changes direction.
[2]
[5]
2. The displacement, in centimetres, of a particle from an origin, O , at time t seconds, is
given by s( t) �sin t � 4tcos
t , 0 �t
� 1.5.
(a) Write down the maximum distance of the particle from O .
(b) Find the acceleration of the particle at the instant it first goes back to O .
[2]
[5]
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