The velocity of a particle moving in the positive direction of $x-$ axis varies as $v=10\sqrt{x}$ ($v$ is in ${\text{ms}}^{-1},x$ is in $m$). Assuming that at $t=0,$ particle was at $x=0$. Then,

Q. The velocity of a particle moving in the positive direction of $x-$ axis varies as $v=10\sqrt{x}$ ($v$ is in ${\text{ms}}^{-1},x$ is in $m$). Assuming that at $t=0,$ particle was at $x=0$. Then,

Q. The velocity of a particle moving in the positive direction of the x axis varies as $V=\alpha \sqrt{x}$ where $\alpha$ is a positive constant. Assuming that at the moment $t=0$ the particle was located at the point $x=0$, find acceleration at $t=51s$.

Q. Velocity in $m/s$ of a particle moving along $x-$axis varies with time as $v=(10+5t-t^2)$. At time $t=0,x=0.$ Acceleration of particle at $t=2s$ is $xm/s^2$, then value of $x$ is

Q. The velocity of a particle moving in the positive direction of the x-axis varies as $V=\alpha \sqrt{x}$ where $\alpha$ is a positive constant. Assuming that at the moment $t=0$ the particle was locate at the point $x=0$, find velocity at $t=2s$.

Q. For a particle moving along $x$ - axis, the acceleration $a$ of the particle in terms of its $x$- coordinate $x$ is given by $a=-9x$, where $x$ is in meters and $a$ is in ${\text{m/s}}^2$. Take acceleration, velocity and displacement in positive $x$ - direction as positive. The initial velocity of particle at $x=0$ is $u=+6\text{m/s}$. The velocity of particle at $x=2\text{m}$ will be