Using definite integrals with velocity and acceleration

Question

Rocket A is traveling 49 ft/sec at 80 seconds. Rocket B is launched upward with an acceleration of $$a(t)=\frac3{\sqrt{t +1}}$$. At time t=0 seconds, the initial height of the rocket is 0 feet, and the initial velocity is 2 feet per second. Which of the two rockets is traveling faster at t=80 seconds?

Answer 1

$a(t) = \frac{dv}{dt}$ where v(t) is the velocity.
Then $v(t) = \int{a(t)dt}$. Use the condition for velocity at $t = 0$ to obtain the integration constant. Then you can get velocity at $t = 80$.