Your Practice Set – Applications and Interpretation for IBDP Mathematics
53
Paper 2 – Problems in Kinematics
Example
A particle moves in a straight line . Its velocity , v ms
� 1
, at time t seconds , is given by v( t) ( 3 )
�t
� .
3
� t � , for 0 6
( a ) Find the velocity of the particle when t � 2.
( b ) Find the value of t for which the particle is at rest .
( c ) Find the total distance the particle travels during the first six 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 positive .
[ 2 ]
[ 3 ]
[ 3 ]
[ 2 ]
[ 3 ]
It is given that the initial displacement of the particle is 81 m . 4
( f ) Find the expression of st (), the displacement of the particle . [ 4 ]
Solution
( a ) The initial velocity � v ( 2 )
3
�( 2 � 3 ) ( M1 ) for substitution
�� 1ms �1 A1
( b ) vt ( ) � 0 ( M1 ) for setting equation
3 ( t �3 ) � 0
|
t �3�
0
|
( A1 ) for correct approach |
|
t �
3
|
A1 |
[ 2 ]
[ 3 ]
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