The velocity $v$ reached by a car of mass $m$ at certain distance from the starting point driven with…

The velocity $v$ reached by a car of mass $m$ at certain distance from the starting point driven with constant power $P$ is such that
  1. $v \propto \frac{3 P}{m}$
  2. $v^2 \propto \frac{3 P}{m}$
  3. $v^3 \propto \frac{2 P}{m}$
  4. $v \propto\left(\frac{3 P}{m}\right)^2$

Solution

$P=\frac{\frac{1}{2} m v^2}{t} \Rightarrow v^2=\frac{2 P t}{m} \Rightarrow v^2 \propto \frac{2 P}{m}$

Asked in: AP EAMCET 2012

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