Question

The velocity of a particle varies with time at $v\left(t\right)=e^{-2\pi t}$. Find the displacement of the particle till $t=(\frac{1}{2\pi })$ sec.

• A. $-\frac{\left(1\right)}{2\pi e}$
• B. $\frac{1}{2\pi e}$e
• C. $\frac{(e-1)}{2\pi e}$
• D. $\frac{1}{e}$

Answer 1

The correct option is C

$\frac{(e-1)}{2\pi e}$

$v=e^{-2\pi t}$

$\frac{dx}{dt}=e^{-2\pi t}$

$\underset{0}{\overset{x}{\int }}dx=\underset{0}{\overset{\frac{1}{2\pi }}{\int }}{e}^{-2\pi dt}$

$\frac{e^{-2\pi t}}{-2\pi }{]}_0^{\frac{1}{2\pi }}$

$x=[\frac{e^{-2\pi t}-2\pi }{+}\frac{1}{-2\pi }]$

$x=\frac{1\left(e^{-1}\right)}{-2\pi }+\frac{1}{2\pi }$

$\frac{1}{2\pi }[1-\frac{1}{e}]$

$x=\frac{(e-1)}{2\pi e}$