The velocity of an object is given by $v = kt$,where $k = 2 \, m/s^2$. What distance (in $m$) will it cover in the first $3 \, s$?

$A$ body is moving from rest under constant acceleration. Let $S_1$ be the displacement in the first $(p - 1) \ s$ and $S_2$ be the displacement in the first $p \ s$. The displacement in the $(p^2 - p + 1)^{th} \ s$ will be:

If the velocity of a particle moving along the $x-$ axis is given by $v = k\sqrt{x}$,then which of the following is true? ($a$ is acceleration)

The position $x$ of a particle at any instant is related to its velocity $v$ by the equation $v = \sqrt{2x + 9}$. The particle starts from the origin. What are the initial acceleration and initial velocity of the particle?

$A$ $150 \,m$ long train is moving with a uniform velocity of $45 \,km/h$. The time taken by the train to cross a bridge of length $850 \,m$ is..........$sec$.

The relation between time $t$ and displacement $x$ is $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. If $v$ is the velocity,the retardation is: