Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 53
1 . A particle moves in a straight line . Its velocity , v ms
� 1
, at time t seconds , is given by v( t) ( t 4 )
�t
� .
3
� � � , for 0 8
( a ) Find the initial velocity .
( b ) Find the value of t for which the velocity of the particle is
� 27 ms �1 .
( c ) Find the total distance the particle travels during the first seven seconds .
( d ) Find the expression of at (), the acceleration of the particle .
( e ) Find all possible values of t for which the velocity and acceleration are both negative .
It is given that the initial displacement of the particle is 28 m .
( f ) Find the expression of st (), the displacement of the particle .
[ 2 ]
[ 3 ]
[ 3 ]
[ 2 ]
[ 3 ]
[ 4 ]
2 . A particle moves in a straight line . Its initial displacement is zero metres . Its velocity , v ms
� 1
, at time t seconds , is given by
v t � � t � t � t � , for 0�t
� 4.
3 2 ( ) 2 12 24 16
( a ) Find the expression of st (), the displacement of the particle .
( b ) Find the exact value of the displacement of the particle at t � 3.3 .
( c ) Find the total distance the particle travels during the first 3.3 seconds .
( d ) Find the expression of at (), the acceleration of the particle . [ 2 ]
( e ) Find all possible values of t for which the velocity is positive and the acceleration is negative . [ 3 ]
[ 4 ]
[ 2 ]
[ 3 ]
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