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Displacement equation is written in the form of below mention mathematicle equation-

\mathrm{S(t)=(\alpha+\beta) t^{2 n}}

Rate of change of velocity is varies as ;-

Option: 1

\mathrm{t^{2 n+2}}


Option: 2

\mathrm{t^{2 n-1}}


Option: 3

\mathrm{t^{2(n-1)}}


Option: 4

\mathrm{t}


Answers (1)

best_answer

Given, Displacement \mathrm{s(t)=(\alpha+\beta) t^{2 n}}

Rate of change of velocity is known as acceleration.

Firstly calculate the velocity -

                                \mathrm{\begin{aligned} v=\frac{d s}{d t} & =\frac{d}{d t}(\alpha+\beta) t^{2 n-1} \\ & =\left(\alpha+\beta \frac{d t}{d t}\right. \\ & =(\alpha+\beta)(2 n) t^{2 n-1}-(1) \end{aligned}}

Now, calculate the acceleration 

                                             \mathrm{\begin{aligned} & a=\frac{d l}{d t} \\ & a=\frac{d}{d t}\left[(\alpha+\beta) \cdot 2 n t^{2 n-1}\right] \\ & a=(\alpha+\beta) 2 n(2 n-1) t^{2 n-2} \\ & a \propto t^{2 n-2} \\ & a \propto t^{2(n-1)} \quad \end{aligned}}

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Anam Khan

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