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Velocity of the particle is  \mathrm{V=\frac{\alpha}{2} t^2}, where \alpha  is constant. The displacement of the particle at  \mathrm{t=1 \mathrm{sec}}

Option: 1

\alpha / 2


Option: 2

\alpha / 6


Option: 3

\alpha / 3


Option: 4

\alpha


Answers (1)

best_answer

Given,  v=\frac{\alpha}{2} t^2

Displacement s  =\int_0^t v d t \\
s =\int_0^1 \frac{\alpha}{2} t^2 d t \\
s =\frac{\alpha}{2} \int_0^1 t^2 d t=\left.\frac{\alpha}{2} \frac{t^3}{3}\right|_0 ^1 \\
s =\frac{\alpha}{2} \times \frac{1}{3}=\frac{\alpha}{6}

Posted by

Ritika Jonwal

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