A particle has initial velocity $\left( {2\hat i + 3\hat j} \right)$ and acceleration $\left( {0.3\hat i + 0.2\hat j} \right)$. The magnitude of velocity after $10\, seconds$ will be 

A horizontal plane supports a stationary vertical cylinder of radius $R = 1\ m$ and a disc $A$ attached to the cylinder by a horizontal thread $AB$ of length $l_0 = 2\ m$ (seen in figure, top view). An intial velocity ($v_0 = 1\ m/s$) is imparted $AB$ to the disc as shown in figure. .......... $\sec$ long will it move along the plane until it strikes against the cylinder ? (All surface are assumed to be smooth)

“Explain average acceleration and instantaneous acceleration.”

Which two motions are considered to be combined for motion in plane ?

A $NCC$ parade is going at a uniform speed of $9\,km / h$ under a mango tree on which a monkey is sitting at a height of $19.6\,m$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is $...m$

(Given $g=9.8\,m / s ^{2}$ )

A particle starts from the origin at $t=0$ $s$ with a velocity of $10.0 \hat{ j } \;m / s$ and moves in the $x-y$ plane with a constant acceleration of $(8.0 \hat{ i }+2.0 \hat{ j }) \;m \,s ^{-2} .$

$(a)$ At what time is the $x$ - coordinate of the particle $16\; m ?$ What is the $y$ -coordinate of the particle at that time?

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