Analysis and Approaches HL Practice Paper Book

Analysis and Approaches HL Practice Paper Book | Page 150

11 . A particle moves in a straight line . Its initial displacement is velocity , v ms

� 1

, at time t seconds , is given by

�

� metres . Its 2

�t 0�t

�1

� 1 t v( t) � �

�� e ^� 1� t � 5 .

� � 0 otherwise

( a ) Find the expression of st (), the displacement of the particle .

( b ) Find all possible values of t for which the acceleration is less than � 3 ms ^�2 .

( c ) Show that , for 1�t � 5,

[ 8 ]

[ 4 ]

( i )

( ii ) ds

1 dv ^�� ^;

dt 1 e dv

� t�1

�� . [ 4 ]