$A$ man moves in the $x-y$ plane along the path shown. At what point is his average velocity vector in the same direction as his instantaneous velocity vector? The man starts from point $P$.

$A$ body moves $6\,m$ north,$8\,m$ east,and $10\,m$ vertically upwards. What is its resultant displacement from the initial position?

$A$ particle moves in the $x-y$ plane with velocity $\vec{v} = a\hat{i} + bx\hat{j}$,where $a$ and $b$ are constants. If the particle was initially at the origin,find the equation of its trajectory.

Position of an ant ($S$ in metres) moving in $Y-Z$ plane is given by $S = 2t^2 \hat{j} + 5 \hat{k}$ (where $t$ is in seconds). The magnitude and direction of velocity of the ant at $t = 1 \ s$ will be:

$A$ hall has the dimensions $10\,m \times 12\,m \times 14\,m$. $A$ fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement in meters?

At time $t = 0$,a particle starts travelling from a height of $7 \, \text{cm}$ along the $z$-axis in a plane,keeping the $z$-coordinate constant. At any instant of time,its positions along the $x$ and $y$ directions are defined as $x = 3t$ and $y = 5t^3$ respectively. What will be the acceleration of the particle at $t = 1 \, \text{s}$?