A) \[2\hat{i} + 3\hat{j}\]
B) \[4\hat{i} + 6\hat{j}\]
C) \[18\hat{i} + 6\hat{j}\]
D) None of these
Correct Answer: C
Solution :
Here, \[\operatorname{F}=6{{t}^{2}}\hat{i}\,\,+\,\,4t\,\hat{j}\] \[m=3\,kg\] \[\therefore \,\,\,\,\,\,Acceleration\,\,\,a=\frac{F}{m}=\frac{6{{t}^{2}}\,\hat{i}+4t\,\hat{j}}{3}=2{{t}^{2}}\,\hat{i}+\frac{4}{3}t\,\hat{j}\]As, \[a=\frac{dv}{dt}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,dv=adt=(2{{t}^{2}}\,\hat{i}\,\,+\,\,\frac{4}{3}t\,\hat{j})\,dt\] \[\int{dv=\int_{0}^{3}{\left( 2{{t}^{2}}\,\hat{i}+\frac{4}{3}\,{{t}^{2}}\,\hat{j} \right)}\,\,}dt\] \[v=\left[ \frac{2}{3}{{t}^{3}}\,\hat{i}\,\,+\,\,\frac{4}{6}{{t}^{2}}\,\hat{j}\, \right]_{0}^{3}\] \[v\,\,=\,\,18\,\hat{i}\,\,+\,\,6\,\hat{j}\]
You need to login to perform this action.
You will be redirected in
3 sec
