The position of of a particle is given by `vec r =3.0 t hat I + 2.0 t^(2) hat j+ 5.0 hat k` wher (t) in seconds and the coefficients mave the proper units for `ve r` to ber in metres. Find the velocity and acceleration of the particle in magnitude and direction at time `t=3.0 s`

Explanation

To solve the problem, we need to find the velocity and acceleration of the particle given its position vector \(\vec{r} = 3.0 \hat{i} + 2.0 t^2 \hat{j} + 5.0 \hat{k}\) at time \(t = 3.0\) seconds.

### Step 1: Find the Velocity Vector
The velocity vector \(\vec{v}\) is the time derivative of the position vector \(\vec{r}\).

\[ \vec{v} = \frac{d\vec{r}}{dt} \]
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