12 . A particle moves in a straight line with acceleration a ms
�2 and velocity v ms
� At time t s , 0 �t
� , the acceleration is given by the differential equation 40 da
2
2a
50 dt � � . The initial acceleration and the initial velocity are 2
5 ms � and
1 4 1 ln 2 ms � respectively .
� 1
.
( a ) Find a in terms of t . [ 7 ]
( b ) Find v in terms of t . [ 7 ]
2
1 �a
� 25 � ( c ) Show that v � ln � �
4 � 25 � . [ 4 ]
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