A projectile is thrown into space so as to have maximum horizontal range $R$. Taking the point of projection as origin, the coordinates of the points where the speed of the particle is minimum are-

- A
$(R, R)$

- B
$\left( {R,\frac{R}{2}} \right)$

- C
$\left( {\frac{R}{2},\frac{R}{4}} \right)$

- D
$\left( {R,\frac{R}{4}} \right)$

A particle is moving on a circular path of radius $r$ with uniform velocity $v$. The change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = {40^o})$

If the instantaneous velocity of a particle projected as shown in figure is given by $v =a \hat{ i }+(b-c t) \hat{ j }$, where $a, b$, and $c$ are positive constants, the range on the horizontal plane will be

During which time interval is the particle described by these position graphs at rest?

A particle is projected from a horizontal plane such that its velocity vector at time $t$ is given by $\vec v = a\hat i + (b - ct)\hat j$ . Its range on the horizontal plane is given by

A particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where $g$ is acceleration due to gravity)