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  • A particle is moving with velocity v is given by the equation - <img alt="\mathrm{ v=40 t^2+20 t+4 }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20v%3D40%20t%5

A particle is moving with velocity v is given by the equation -

\mathrm{ v=40 t^2+20 t+4 }
what time when acceleration will be \mathrm{40 \mathrm{~m} / \mathrm{s}^2}?

Option: 1

\mathrm{1 / 2 \, \mathrm{sec}}


Option: 2

\mathrm{1 / 8 \mathrm{sec}}\, \, \, \, \, \, \,\,


Option: 3

\mathrm{1 / 6\, \mathrm{sec}}


Option: 4

\mathrm{1 / 4\, \mathrm{sec}}


Answers (1)

best_answer

Given, \mathrm{v=40 t^2+20 t+4}

Acceleration \mathrm{a=\frac{d v}{d t}=\frac{d}{d t}\left[40 t^2+20 t+4\right]}

                                  \mathrm{ a=\80t +20-0 }                ......(1)

but in question acceleration \mathrm{a=40 \mathrm{~m} / \mathrm{s}^2}, then time t will become-

\mathrm{ \begin{aligned} 40 & =80 t+20 \\ 40-20 & =80 t \\ t \Rightarrow t=\frac{1}{4} \mathrm{sec} \text { Ans. } \end{aligned} }

Posted by

vishal kumar

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