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AAI JE (Technical) Official Paper 2018

Option 1 : 2αv^{3}

ST 2: Strength of materials

2149

15 Questions
15 Marks
15 Mins

**Concept:**

Given, t = αx2 + βx

Differentiating the above equation with respect to x,

\(\frac{dt}{dx}=2α x+b\) .......(1)

We, know that the rate of change of displacement with respect to time is velocity, V = \(\frac{dx}{dt}\)

From equation 1.

\(V =\frac{1}{2α x\;+\;b}\) .......(2)

The rate of change of velocity with respect to time is acceleration or retardation(a),

Differentiating equation 2 with respect to time,

\(V =\frac{1}{2α x\;+\;b}\)

\(a=\frac{dV}{dt}=-\frac{1}{(2α x\;+\;b)^2}\times(2α\;\times\frac{dx}{dt})\)

\(a=\frac{dV}{dt}=-\frac{1}{(2α x\;+\;b)^2}\times(2α\;\times V)\) .......(3)

From equation 2 and 3.

a = -2αV^{3}

Hence, Retardation = 2αV3