Question

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, the depth of the shaft is

• A. $\frac{{at}^2}{4}$
• B. $\frac{{at}^2}{3}$
• C. $\frac{{at}^2}{2}$
• D. $\frac{{at}^2}{8}$

Answer 1

The correct option is B $\frac{{at}^2}{3}$

We have $t_1=\frac{v}{a}$ and $t_2=\frac{v}{2a}$
Adding both times, we get
$t=\frac{3v}{2a}$...... (1)
or
$h=h_1+h_2$

$h=\frac{v^2}{2a}+\frac{v^2}{4a}$

$h=\frac{3v^2}{4a}$...... (2)

From (1) and (2), we get

$h=\frac{a{t}^2}{3}$