Question

The acceleration of an object is given by a(t) =$cos\pi tm{s}^{-2}$ and its velocity at time t = 0 is $\frac{1}{2\pi }m{s}^{-1}$ at origin. Its velocity at $t=\frac{3}{2}s$ is

• A. $-\frac{1}{2\pi }m{s}^{-1}$
• B. $\frac{3}{2\pi }m{s}^{-1}$
• C. $\frac{1}{\pi }m{s}^{-1}$
• D. $\frac{2}{\pi }m{s}^{-1}$

Answer 1

The correct option is A $-\frac{1}{2\pi }m{s}^{-1}$

$Givena\left(t\right)=cos\pi tm{s}^{-2}\frac{dv}{dt}=a\left(t\right)\Rightarrow {\int }_{\frac{1}{2\pi }}^{v}v={\int }_0^{t}cos\pi tdtv-\frac{1}{2\pi }=\frac{sin\pi t}{\pi }nowatt=\frac{3}{2}sv=-\frac{1}{2\pi }m{s}^{-1}$