$A$ smooth circular groove has a smooth vertical wall as shown in the figure. $A$ block of mass $m$ moves against the wall with a speed $v$. Which of the following curves represents the correct relation between the normal reaction $(N)$ on the block by the wall and the speed of the block $(v)$?

$A$ particle of mass $m$ moves along a circular path of constant radius $r$. The centripetal acceleration of the particle $a_c$ varies with time $t$ as $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

The figure shows the velocity and the acceleration of a point-like body at the initial moment of its motion. The direction and the absolute value of the acceleration remain constant. Find the time when the speed becomes minimum. (Given: $a = 4\, m/s^2$,$v_0 = 40\, m/s$,$\phi = 143^o$)

$A$ particle is projected from the ground with velocity $u$ at an angle $\theta$ with the horizontal. The horizontal range,maximum height,and time of flight are $R, H$,and $T$ respectively. They are given by $R = \frac{u^2 \sin 2\theta}{g}$,$H = \frac{u^2 \sin^2 \theta}{2g}$,and $T = \frac{2u \sin \theta}{g}$. Now,keeping $u$ fixed,$\theta$ is varied from $30^o$ to $60^o$. Then,

$A$ particle moves with a constant speed of $5 \, ms^{-1}$ as shown in the figure. What is the change in velocity during half a revolution in $ms^{-1}$?

$A$ projectile is thrown at an angle $\theta$ to the horizontal from $O$ and it hits the ground at $O'$. During the entire motion (select the wrong statement):