Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 34
1 . A particle A is moving on a x - y plane . The displacement of A in the first 5 seconds is �10
� t � given by s
A
� � � , where t is the time in seconds after the start of motion . � 2t
�
( a ) Write down the vector equation for the displacement of A , giving the answer in the form r �a �tb . [ 2 ]
( b ) Find the coordinates of A 5 seconds after the start of motion . [ 2 ]
A starts to change its velocity such that the velocity of A after t � 5 is given by ��4� v
A
� � � . ��2�
( c ) Find the coordinates of A
( i ) 7 seconds after it changes its velocity ;
( ii ) 20 seconds after the start of motion . [ 4 ]
A collides with the another particle B at t � 20. It is given that B travels at a constant ��1�
velocity v
B
� � � . ��1�
( d ) Find the coordinates of B at t � 0.
( e ) Hence , write down the vector equation for the displacement of B , giving the answer in the form r �a �tb .
( f ) Find the distance between the two particles 8 seconds before they collide .
[ 2 ]
[ 2 ]
[ 3 ]
2 . A ball A is moving on a smooth table which can be modelled by a x - y plane . Its initial position is ( 3 , 4 ) . A collides with another stationary ball B after 1 second , and the initial position of B is ( 15 , 9 ) .
( a ) Find the initial distance between the two balls . [ 2 ]
( b ) Write down the vector equation for the displacement of A , giving the answer in the form r �a �tb , where t is the time in seconds after the start of motion . [ 2 ]
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