question_answer

A self-propelled vehicle of mass m whose engine delivers a constant power P has an acceleration \[a=\frac{P}{mv}\]What is the distance travelled by it (assuming no friction) to mv increase the velocity of the vehicle from \[V\,\,\,to\,\,{{\,}_{1}}{{V}_{2}}\]?

A)   \[x=\frac{3m}{P}(V_{2}^{3}-V_{1}^{3})\]      

B)  \[x=\frac{m}{3P}(V_{2}^{3}-V_{1}^{3})\]

C)  \[x=\frac{2m}{P}(V_{2}^{3}-V_{1}^{3})\]

D)  \[x=\frac{m}{2P}(V_{2}^{3}-V_{1}^{3})\]