as acceleration depending on time so its not a
case of constant acceleration hence $\overrightarrow{v}=\int_{0}^{i} \vec{a} \mathrm{d} t$
$\therefore \quad \overrightarrow{\mathrm{v}}=\int_{0}^{3}\left(\frac{6 \mathrm{t}^{2}}{3} \hat{\mathrm{i}}+\frac{4 \mathrm{t}}{3} \hat{\mathrm{j}}\right) \mathrm{dt}$
$=\left[\frac{6 t^{3}}{9} \hat{i}+\frac{4 t^{2}}{6} \hat{j}\right]_{0}^{3}=18 \hat{i}+16 \hat{j}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$(I)$ Energy of one molecule at absolute temperature is zero
$(II)$ $r .m.s.$ speeds of different gases are same at same temperature
$(III)$ For one gram of all ideal gas kinetic energy is same at same temperature
$(IV)$ For one mole of all ideal gases mean kinetic energy is same at same temperature