A lift performs the first part of its ascent with uniform acceleration $a$ and the remaining with uniform retardation $2a$. If $t$ is the time of ascent, find the depth of the shaft.
$\frac{a t^2}{4}$
$\frac{a t^2}{3}$
$\frac{a t^2}{2}$
$\frac{a t^2}{8}$
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
If the velocity of a body related to displacement ${x}$ is given by $v=\sqrt{5000+24 {x}} \;{m} / {s}$, then the acceleration of the body is $\ldots \ldots {m} / {s}^{2}$