Section B ( 53 marks ) 10 . A marble is moving along a straight track with initial velocity
1
30 cms � . It decelerates in two stages . In the first stage , the marble decelerates at the
1 constant rate so that its velocity after 2s is 20 cms � . Let v 1 () t , 0�t
� 2, be the velocity function of the marble in the first stage .
( a ) |
( i ) |
Show that the acceleration function of the marble in the first |
|
|
stage is (
5
1
|
( ii ) Hence , write down the expression of v 1
() t .
( b ) Find the total distance the marble travelled in the first stage .
0.2
Let v ( ) 20 b t
2 t � e � , 2 �t� c be the velocity function of the marble in the second stage . It is given that the total distances the marble travelled in two stages are equal .
[ 4 ]
[ 3 ]
( c ) ( i ) Show that b � 0.4 .
( ii ) Hence , find c . [ 7 ]
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