Exercise 45
1 . The displacement , in centimetres , of a particle from an origin , O , at time t seconds , is given by
� , 0 �t � 2.5 .
2 s( t) t cos t
( a ) Find the maximum distance of the particle from O .
( b ) ( i ) Find s� () t .
[ 2 ]
( ii ) Find the time when the particle first changes direction .
( iii ) Hence , write down the acceleration of the particle at the instant it first changes direction .
[ 5 ]
2 . The displacement , in centimetres , of a particle from an origin , O , at time t seconds , is given by s( t) � 4t cos t , 0 �t � 2.25 .
( a ) Find the maximum distance of the particle from O .
( b ) ( i ) Find the time when the particle first goes back to O .
[ 2 ]
( ii ) Find s� () t .
( iii ) Hence , write down the acceleration of the particle at the instant it first goes back to O .
3 . The displacement , in centimetres , of a particle from an origin , O , at time t seconds , is given by s( t) �t � sin ( e t ) , 0 �t � 2.8 .
[ 5 ]
10
( a ) Find vt (), the velocity of the particle at time t seconds .
( b ) ( i ) Find the time when the particle changes direction for the 4th time .
[ 3 ]
( ii ) Hence , write down the acceleration of the particle at the instant it changes direction for the 4th time .
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