The acceleration of a particle varies with time t as
`a=t^(2)+t+2`
where t is in seconds.
The particle starts with an initial velocity v-3m/s at t=0. find the velocity of the particle at the end of 5s.

Explanation

To find the velocity of the particle at the end of 5 seconds given the acceleration function \( a(t) = t^2 + t + 2 \) and the initial velocity \( v(0) = 3 \, \text{m/s} \), we can follow these steps:

### Step 1: Write the relationship between acceleration and velocity
Acceleration \( a \) is the rate of change of velocity \( v \) with respect to time \( t \):
\[ a = \frac{dv}{dt} \]
Substituting the given acceleration function, we have:
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