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A particle moves along a curve in the xy-plane with an acceleration $<-3, 2t>$.

If the velocity is $<10, -5>$ and the position is $<0,1>$ at time $t = 0$, find an expression for the position of the particle for all times $t \gt 0$.

A

$<-\cfrac{3{ t }^{ 2 }}{2}+10t-1,\ \cfrac{{ t }^{ 3 }}{3}-5t>$

B

$<-\cfrac{3{ t }^{ 2 }}{2}+10t+1,\ \cfrac{{ t }^{ 3 }}{3}-5t>$

C

$<-\cfrac{3{ t }^{ 2 }}{2}+10t,\ \cfrac{{ t }^{ 3 }}{3}-5t-1>$

D

$<-\cfrac{3{ t }^{ 2 }}{2}+10t,\ \cfrac{{ t }^{ 3 }}{3}-5t+1>$

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