A self – propelled vehicle of mass m whose engine deliv

A self – propelled vehicle of mass m, whose engine delivers a constant power P, has an acceleration a = (P/mv). (Assume that there is no friction). In order to increase its velocity from $v_{1}$ to $v_{2}$ , the distance it has to travel will be:

$\frac{m}{3 P} (v_{2} - v_{1})^{3}$

$\frac{m}{3 P} (v_{2}^{2} - v_{1}^{2})$

$\frac{m}{3 P} (v_{2}^{3} - v_{1}^{3})$

$\frac{3 P}{m} (v_{2}^{2} - v_{1}^{2})$

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Right Answer is: C

SOLUTION

$= \frac{v d v}{d x} = \frac{P}{m v}$

$\int_{v_{1}}^{v_{2}} v^{2} d v = \int_{0}^{x} P d x$

$P x = \frac{m}{3} (v_{2}^{3} - v_{1}^{3}) \Rightarrow x = \frac{m}{3 P} (v_{2}^{3} - v_{1}^{3})$

A self – propelled vehicle of mass m whose engine deliv

Right Answer is: C

SOLUTION

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