The initial velocity of a particle moving along $x$-axis is $u$ (at $t=0$ and $x=0$ ) and its acceleration $a$ is given by $a=k x$. Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?

The relation between time $t$ and distance $x$ for a moving body is given as $t=m x^{2}+n x$, where ${m}$ and ${n}$ are constants. The retardation of the motion is -

(Where $v$ stands for velocity)

The displacement of a particle, moving in a straight line, is given by $s = 2{t^2} + 2t + 4$ where $s$ is in metres and $t$ in seconds. The acceleration of the particle is........$ms^{-2}$

For the acceleration-time $(a-t)$ graph shown in figure, the change in velocity of particle from $t=0$ to $t=6 \,s$ is ........ $m / s$

The velocity- displacement graph of a particle is shown in figure.

$(a)$ Write the relation between $v$ and $x$.

$(b)$ Obtain the relation between acceleration and displacement and plot it.

Your friend driving his car overtakes your car on the highway. Which of the following statement must be true at the instant he is passing you? Assume the cars as point particles.