Rectilinear Motion

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Question

A lift performs the first part of its ascent with uniform acceleration a and the remaining with uniform retardation 2a and stops. If t is the time of ascent, the depth of the shaft is $\frac{{at}^{2}}{n}$ . Find value of n.

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Solution

If t₀ is the time during acceleration, then $\frac{t_{0}}{2}$ will be the time during retardation.
Now, $t_{0} + \frac{t_{0}}{2} = t$
$\begin{array}{l} ∴ t_{0} = \frac{2 t}{3} and \frac{t_{0}}{2} = \frac{t}{3} \\ s = \frac{1}{2} a {(\frac{2 t}{3})}^{2} + \frac{1}{2} \times 2 a \times {(\frac{t}{3})}^{2} \\ = \frac{{at}^{2}}{3} \end{array}$

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Rectilinear Motion

Remember concepts with our Masterclasses.

A lift performs the first part of its ascent with uniform acceleration a and the remaining with uniform retardation 2a and stops. If t is the time of ascent, the depth of the shaft is at2n. Find value of n.

If t0 is the time during acceleration, then t02 will be the time during retardation.Now, t0+t02=t ∴ t0=2t3 and t02=t3s=12a2t32+12×2a×t32=at23

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A lift performs the first part of its ascent with uniform acceleration a and the remaining with uniform retardation 2a and stops. If t is the time of ascent, the depth of the shaft is $\frac{{at}^{2}}{n}$ . Find value of n.