Position vector `vec(r)` of a particle varies with time t accordin to the law `vec(r)=(1/2 t^(2))hat(i)-(4/3t^(1.5))hat(j)+(2t)hat(k)`, where r is in meters and t is in seconds.
(a) Find suitable expression for its velocity and acceleration as function of time (b) Find magnitude of its displacement and distance traveled in the time interval `t=0` to `4 s`.

Explanation

To solve the problem step by step, we will break it down into parts (a) and (b) as per the question.

### Part (a): Finding Velocity and Acceleration

1. **Given Position Vector**:
The position vector of the particle is given by:
\[
\vec{r}(t) = \frac{1}{2} t^2 \hat{i} - \frac{4}{3} t^{1.5} \hat{j} + 2t \hat{k}
...