$A$ body lying initially at point $(3,7)$ starts moving with a constant acceleration of $4 \hat{i}$. Its position after $3 \,s$ is given by the coordinates ..........

The initial velocity of a particle is $u$ (at $t = 0$) and the acceleration is given by $a(t) = at$. Which of the following relations is valid?

The velocity $(v)$ of a particle starting from rest increases linearly with time $(t)$ as $v = 4t$,where $v$ is in $m s^{-1}$ and $t$ is in seconds. The distance covered by the particle in the first $4$ seconds is (in $m$)

$A$ particle located at $x= 0$ at time $t= 0$ starts moving along the positive $x-$direction with a velocity $v$ that varies as $v = \alpha \sqrt{x}$. The displacement of the particle varies with time as:

$A$ particle moves according to the equation $x = at^2 - bt^3$. At what time will its acceleration be zero?

$A$ particle with initial velocity $v_0$ moves with constant acceleration $a$ in a straight line. Find the distance travelled in the $n^{th}$ second.