$A$ particle has an initial velocity $(3\hat{i} + 4\hat{j})$ and an acceleration of $(0.4\hat{i} + 0.3\hat{j})$. Its speed after $10\,s$ is:

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

$A$ ball is projected from a point with a speed $V_0$ at a certain angle $\theta$ with the horizontal. From the same point and at the same instant,a person starts running with a constant speed $0.5 V_0$ to catch the ball. If the person catches the ball after some time,then the angle of projection of the ball is (in $^{\circ}$)

The position vector of a particle is given as $\vec{r} = (t^2 - 4t + 6)\hat{i} + (t^2)\hat{j}$. The time after which the velocity vector and acceleration vector become perpendicular to each other is equal to ....... $sec$.

$A$ particle is moving in the $xy$-plane and crosses the origin at time $t=0$. The equation of motion of the particle is $y=4x^2$. If the velocity of the particle is $\vec{v}=(2\hat{i}+2\hat{j}) \text{ m s}^{-1}$ and acceleration is $\vec{a}=(a\hat{j}) \text{ m s}^{-2}$, then the magnitude of $a$ is

$A$ 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?