4 . A particle moves in a straight line . Its velocity , given by v ms
� 1
, at time t seconds , is v( t) 0.5 ( t 5 ) �t
� .
3 � � � , for 0 10
( a ) Find the initial velocity .
( b ) Find the value of t for which the velocity of the particle is � 13.5 ms �1 .
[ 3 ] ( c ) Find the total distance the particle travels during the first ten seconds .
[ 3 ]
( d ) Find the expression of at (), the acceleration of the particle . [ 2 ]
( e ) Find all possible values of t for which the velocity and acceleration are both non-negative .
[ 3 ]
It is given that the initial displacement of the particle is � 78 m .
[ 2 ]
( f ) Find the expression of st (), the displacement of the particle . [ 4 ]
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