A) \[{{\operatorname{t}}^{2}}{{p}_{o}}\]
B) \[{{\operatorname{t}}^{1/2}}\]
C) \[{{\operatorname{t}}^{-1/2}}\]
D) \[\frac{t}{\sqrt{m}}\]
Correct Answer: B
Solution :
[b] Constant power of car \[{{P}_{0}}=F.V=ma.v\] \[{{P}_{0}}=m\frac{dv}{dt}.v\] \[{{P}_{0}}dt=mvdv\] Integrating \[{{P}_{0}}.t=\frac{m{{v}^{2}}}{2}v=\sqrt{\frac{2{{P}_{0}}t}{m}}\] \[\because ~~{{P}_{0}},\]m and 2 are constant \[\therefore \text{ }v\text{ }\propto \sqrt{t}\]
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