What can be the angle between velocity and acceleration for the motion in two or three dimension ?

The position of a particle is given by

$r=3.0 t \hat{i}+2.0 t^{2} \hat{j}+5.0 \hat{k}$

where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.

$(a)$ Find $v (t)$ and $a (t)$ of the particle.

$(b)$ Find the magnitude and direction of $v (t)$ at $t=1.0 s$

A body lying initially at point $(3,7)$ starts moving with a constant acceleration of $4 \hat{i}$. Its position after $3 \,s$ is given by the co-ordinates ……….

A man wants to reach from $A$ to the opposite corner of the square $C$. The sides of the square are $100\, m$. A central square of $50\, m\,\times \,50\, m$ is filled with sand. Outside this square, he can walk at a speed $1\,ms^{-1}$. In the central square, he can walk only at a speed of $v\,ms^{-1}$ $(v < 1)$. What is smallest value of $v$ for which he can reach faster via a straight path through the sand than any path in the square outside the sand ?