The velocity- time graph of a body falling from rest under gravity and rebounding from a solid surface is represented by which of the following graphs?

Two particles are projected simultaneously in the same vertical plane, from the same point on ground, but with same speeds but at different angles $( < 90^o )$ to the horizontal. The path followed by one, as seen by the other, is

Which physical quantity can be found by first differntiation and second differentiation of position vector ?

A man on a rectilinearly moving cart, facing the direction of motion, throws a ball straight up with respect to himself

A mosquito is moving with a velocity $\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \,s$ ?

A particle moves along a parabolic path $y=9 x^2$ in such a way that the $x$ component of velocity remains constant and has a value $\frac{1}{3}\,m / s$. The acceleration of the particle is $.......m / s ^2$