Physics - NLM Question with Solution | TestHub

Given that$\overrightarrow{\mathrm{r}}=3\mathrm{t}\hat{\mathrm{i}}-4\cos \mathrm{t}\hat{\mathrm{j}}$

$\frac{\mathrm{d}\overrightarrow{\mathrm{r}}}{\mathrm{dt}}=3\hat{\mathrm{i}}+4\sin \mathrm{t}\hat{\mathrm{j}}$

$\Rightarrow \mathrm{ }\frac{{\mathrm{d}}^2\overrightarrow{\mathrm{r}}}{{\mathrm{dt}}^2}=+4\cos \mathrm{t}\hat{\mathrm{j}}$

Impulse$=\int \overrightarrow{\mathrm{F}}.\mathrm{dt}={\int }_0^{\frac{\mathrm{\pi }}{2}}\mathrm{m}\overrightarrow{\mathrm{a}}\mathrm{dt}={\int }_0^{\frac{\mathrm{\pi }}{2}}\mathrm{m}\left(4\cos \mathrm{t}\hat{\mathrm{j}}\right).\mathrm{dt}$

$=\hat{\mathrm{j}}{\int }_0^{\frac{\mathrm{\pi }}{2}}12\cos \mathrm{t}.\mathrm{dt}=12\hat{\mathrm{j}} \mathrm{N} \mathrm{s}$