The acceleration a in `ms^-2` of a particle is given by `a=3t^2+2t+2`, where t is the time. If the particle starts out with a velocity `v=2ms^-1` at `t=0`, then find the velocity at the end of `2s`.

Explanation

To solve the problem, we need to find the velocity of a particle given its acceleration as a function of time and its initial velocity. The acceleration is given by:

\[ a = 3t^2 + 2t + 2 \]

### Step 1: Understand the relationship between acceleration and velocity
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, this can be expressed as:

\[ a = \frac{dv}{dt} \]
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