A body initially at rest is moving with uniform acceleration $a$ . Its velocity after $n$ seconds is $v$ . The displacement of the body in last $2\,s$ is
$\frac{{2v(n - 1)}}{n}$
$\frac{{v(n - 1)}}{n}$
$\frac{{v(n + 1)}}{n}$
$\frac{{2v(n + 1)}}{n}$
A body starts from origin and moves along $x$-axis so that its position at any instant is $x=4 t^2-12 t$ where $t$ is in second and $v$ in m/s. What is the acceleration of particle is ............. $m / s ^2$
A particle starts from rest and traverses a distance $l$ with uniform acceleration, then moves uniformly over a further distance $2 l$ and finally comes to rest after moving a further distance $3 l$ under uniform retardation. Assuming entire motion to be rectilinear motion the ratio of average speed over the journey to the maximum speed on its ways is