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Standard X

History

German Invasion of the Soviet Union

A lift perfor...

Question

A lift performs the first part of ascent with uniform acceleration $a$ and the remainder with uniform retardation $2 a$ . The lift starts from rest and finally comes to rest. If $t$ is the time of ascent. Find the height ascended by lift.

\frac{a t^{2}}{8}

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\frac{a t^{2}}{4}

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\frac{a t^{2}}{2}

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\frac{a t^{2}}{3}

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Solution

The correct option is D $\frac{a t^{2}}{3}$
Draw a labelled diagram.

Find the height ascended by lift.
Area of the $Δ O A B = \frac{1}{2} \times O B \times A M$
Where, $A M = v$ & $O M = t_{1}$

$t_{1} + t_{2} = O B = t$ & $M B = t_{2}$

$Δ O A B = \frac{1}{2} \times t v = h$
or
$v t = 2 h$ Now, $\frac{v}{t_{1}} = a$
$t_{1} = \frac{v}{a} . . . (i)$
And
$\frac{v}{t_{2}} = 2 a$
$t_{2} = \frac{v}{2 a} . . . (i i)$

Adding (𝑖) and (𝑖𝑖)
$t = t_{1} + t_{2} = \frac{v}{a} + \frac{v}{2 a}$

$= \frac{3 v}{2 a} = \frac{3}{2 a} \times \frac{2 h}{t}$

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

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German Invasion of the Soviet Union

Standard X History

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A lift performs the first part of ascent with uniform acceleration a and the remainder with uniform retardation 2a. The lift starts from rest and finally comes to rest. If t is the time of ascent. Find the height ascended by lift.

A lift performs the first part of ascent with uniform acceleration $a$ and the remainder with uniform retardation $2 a$ . The lift starts from rest and finally comes to rest. If $t$ is the time of ascent. Find the height ascended by lift.