A) \[{{t}^{3/4}}\]
B) \[{{t}^{3/2}}\]
C) \[{{t}^{1/4}}\]
D) \[{{t}^{1/2}}\]
Correct Answer: B
Solution :
[b] We know that \[\operatorname{F}\times v = Power\] \[\therefore \text{ }F\times v=c\]where c = constant \[a\therefore m\frac{dv}{dt}\times v=c~~~\left( \therefore F=ma=\frac{mdv}{dt} \right)\]\[\therefore m\int\limits_{0}^{v}{vdv=c\int\limits_{0}^{t}{dt}\therefore \frac{1}{2}m{{v}^{2}}=ct}\] \[\therefore v=\sqrt{\frac{2c}{m}}\times {{t}^{{}^{1}/{}_{2}}}\] \[\therefore \frac{dx}{dt}=\sqrt{\frac{2c}{m}}\times {{t}^{{}^{1}/{}_{2}}}where\,\,v=\frac{dx}{dt}\] \[\therefore \int\limits_{0}^{x}{dx=\sqrt{\frac{2c}{m}}\times \int\limits_{0}^{t}{{{t}^{{}^{1}/{}_{2}}}}}dt\] \[x=\sqrt{\frac{2c}{m}}\times \frac{2{{t}^{{}^{3}/{}_{2}}}}{3}\Rightarrow x\propto {{t}^{{}^{3}/{}_{2}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
