- Home
- Standard 11
- Physics
4-1.Newton's Laws of Motion
hard
A body of mass $1 \,\, kg$ is acted upon by a force $\vec F = 2\sin 3\pi t\,\hat i + 3\cos 3\pi t\,\hat j$ find its position at $t = 1 \,\, sec$ if at $t = 0$ it is at rest at origin.
A$\left( {\frac{3}{{3{\pi ^2}}},\frac{2}{{9{\pi ^2}}}} \right)$
B$\left( {\frac{2}{{3{\pi ^2}}},\frac{2}{{3{\pi ^2}}}} \right)$
C$\left( {\frac{2}{{3\pi }},\frac{2}{{3{\pi ^2}}}} \right)$
Dnone of these
Solution
$(\vec{f}=2 \sin \pi t i+3 \cos \pi t i$
$\left(\frac{d v}{d t}=2 \sin 3 \pi t i+\cos 3 \pi t j\right.$
$\int \limits_0^\theta d \omega=j \int \limits_0^t 2 \sin 3 \pi t+2 t \cdot t^2 \mid \int \limits_0^t \cos \pi t d t$
$\theta=\left(\left.\frac{-2}{3 \pi} \cdot \cos \pi t i\right.\int\limits_0^t+\left(\frac{3}{3 \pi}\right) \sin 3 \pi t j\right)\int\limits_0^t$
$\left(\frac{d v}{d t}=2 \sin 3 \pi t i+\cos 3 \pi t j\right.$
$\int \limits_0^\theta d \omega=j \int \limits_0^t 2 \sin 3 \pi t+2 t \cdot t^2 \mid \int \limits_0^t \cos \pi t d t$
$\theta=\left(\left.\frac{-2}{3 \pi} \cdot \cos \pi t i\right.\int\limits_0^t+\left(\frac{3}{3 \pi}\right) \sin 3 \pi t j\right)\int\limits_0^t$
Standard 11
Physics
