A particle moves along a line so that its acceleration for $t\geq 0$ is given by $a(t)=\dfrac{t+2}{\sqrt{t^3+3}}$. If the particle's velocity at $t=0$ is $10$, what is the velocity of the particle at $t=5$?

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The change in velocity can be found using:

$$\int\limits_0^5 a(t)   dt$$

The final velocity is:

$$10 + \int\limits_0^5 a(t)=\dfrac{t+2}{\sqrt{t^3+3}}   dt$$ $$\approx 10 + 5.296$$ $$= \boxed{10.296}$$