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

A

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

B

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

C

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

D

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

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