Motion in Straight Line

The position of particle at any instant t is given by relation t = αx 2 + βx + γ. What is the acceleration of the particle? - Wired Faculty

Question

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The position of particle at any instant t is given by relation t = αx² + βx + γ. What is the acceleration of the particle?

Solution

Given,
Position of particle at any insatnt t is,
$straight t equals αx squared plus βx plus straight capital upsilon$
Differentiating both sides w.r.t. tme,
$1 equals 2 ax dx over dt plus straight beta dx over dt$
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Now,
$straight alpha equals straight v fraction numerator d v over denominator d x end fraction space space space equals straight v fraction numerator straight d over denominator d x end fraction left parenthesis 2 alpha x plus straight beta right parenthesis to the power of negative 1 end exponent rightwards double arrow space space space A c c e l e r a t i o n comma space straight alpha equals negative straight nu 2 straight alpha left parenthesis 2 alpha x plus straight beta right parenthesis to the power of negative 2 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space minus 2 alpha nu nu squared space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative 2 a nu cubed$

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