Answer:
Power, \[P=F\upsilon =ma.\upsilon =m\frac{d\upsilon }{dt}.\upsilon \] or \[\upsilon d\upsilon =\frac{P}{m}dt\] Integrating both sides, we get \[\int{\upsilon dt}=\int{\frac{P}{m}dt}=\frac{P}{m}\int{dt}\] [\[\because P,m\]are constant ] or \[\frac{{{\upsilon }^{2}}}{2}=\frac{P}{m}.t\] or \[{{\upsilon }^{2}}=\frac{2P}{m}.t\] or \[\upsilon =\sqrt{\frac{2P}{m}.{{t}^{1/2}}}\] Thus \[\upsilon \propto {{t}^{1/2}}\] Also \[\upsilon =\frac{dx}{dt}\] or \[dx=\upsilon dt=\sqrt{\frac{2P}{m}}.{{t}^{1/2}}dt\] Integrating both sides , we get \[\int_{{}}^{{}}{dx=\sqrt{\frac{2P}{m}}}\int_{{}}^{{}}{{{t}^{1/2}}dt}\] or \[x=\sqrt{\frac{2P}{m}}.\frac{{{t}^{3/2}}}{3/2}=\frac{2}{3}\sqrt{\frac{2P}{m}}.{{t}^{3/2}}\] Thus \[x\propto {{t}^{3/2}}\]
You need to login to perform this action.
You will be redirected in
3 sec