A particle has displacement of $12 \,m$ towards east and $5 \,m$ towards north then $6 \,m $ vertically upward. The sum of these displacements is........$m$

A particle starts from origin at $t=0$ with a velocity $5.0 \hat{ i }\; m / s$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3.0 \hat{ i }+2.0 \hat{ j })\; m / s ^{2} .$

$(a)$ What is the $y$ -coordinate of the particle at the instant its $x$ -coordinate is $84 \;m$ ?

$(b)$ What is the speed of the particle at this time?

The $x$ and $y$ coordinates of the particle at any time are $x = 5t - 2t^2$ and $y = 10t$ respectively, where $x$ and $y$ are in metres and $t$ in seconds. The acceleration of the particle at $t = 2\, s$ is......$m/sec^2$

A man moves in $x-y$ 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 $P$.

“Explain average acceleration and instantaneous acceleration.”