Your Practice Set – Applications and Interpretation for IBDP Mathematics
45
Paper 1 – Problems in Kinematics
Example
The displacement , in centimetres , of a particle from an origin , O , at time t seconds , is given by
� , 0�t
� 3.
3 s( t) t sin t
( a ) Find the maximum distance of the particle from O .
( b ) ( i ) Find s� () t .
[ 2 ]
( ii ) Find the time when the particle first changes direction .
( iii ) Hence , write down the acceleration of the particle at the instant it first changes direction .
[ 5 ]
Solution
( a ) By considering the graph of
( b ) ( i )
the maximum distance � 9.3794925 cm y � t 3 sin t , ( M1 ) for valid approach
� 9.38 cm A1 s� t � t t � t t ( M1 ) for product rule
2 3 ( ) ( 3 )( sin ) ( )( cos ) � � � A1
2 3 s ( t) 3t sin t t cos t
[ 2 ]
( ii ) By considering the graph of 2 3 y 3t sin t t cos t
� � , the particle first changes direction at 2.4556439 s . Thus , the required time is 2.46 s .
( M1 ) for valid approach A1
( iii ) s��( 2.4556439 ) �� 28.04457 cms s
�2
�2
��( 2.4556439 ) �� 28.0 cms A1
[ 5 ]
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