$A$ particle moves in a circle of radius $R$,with a constant speed $v$. Then,during a time interval $t = \pi R / 3v$,which of the following is true?

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: $a = 4\, m/s^2$,$v_0 = 40\, m/s$,$\phi = 143^o$)

$A$ ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy $KE$ of the ball varies with horizontal displacement $x$ as

$A$ body is moving with an initial velocity of $10 \sqrt{2} \ m/s$ in the north-east direction. If it is subjected to an acceleration of $2 \ m/s^2$ directed towards the south, then the velocity of the body after $5 \ s$ is:

$A$ projectile is fired from the surface of the earth with a velocity of $5 \, m s^{-1}$ and angle $\theta$ with the horizontal. Another projectile is fired from another planet with a velocity of $3 \, m s^{-1}$ at the same angle and follows a trajectory which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $m s^{-2}$) (Given $g = 9.8 \, m s^{-2}$):

$A$ projectile is thrown into air with velocity $15 \ m/s$ at an angle $30^{\circ}$ with the horizontal. After what time is its direction of motion perpendicular to its initial direction (in $s$)? (Assume $g = 10 \ m/s^2$)