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Finding Velocity Given Acceleration

APCALC-L9GYBG

If the acceleration of a particle in the xy-plane is $<-2t,t+1>$ and at time $t = 0$, its velocity is $<10,6>$, find the velocity for all times $t > 0$.

A

$<{ t }^{ 2 }-10,\cfrac{1}{2}{ t }^{ 2 }+t-6>$

B

$<{ -t }^{ 2 }+6,\cfrac{1}{2}{ t }^{ 2 }+t+10>$

C

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

D

$<{ -t }^{ 2 }+10,\cfrac{1}{2}{ t }^{ 2 }+t+6>$