Question

A vehicle of mass M is accelerated on a horizontal frictionless road under a force changing its velocity from u to v in distance S. A constant power P is given by the engine of the vehicle, then v =

• A. $\left( u^{3} + \frac{2PS}{M} \right)^{1/3}$
• B. $\left( \frac{PS}{M} + u^{3} \right)^{1/2}$
• C. $\left( \frac{PS}{M} - u^{2} \right)^{1/3}$
• D. $\left( \frac{3PS}{M} + u^{3} \right)^{1/3}$

Answer 1

Answer: (D)

$\left( \frac{3PS}{M} + u^{3} \right)^{1/3}$

Answer 2

Using P = Fv = M$\left( \frac{dv}{dt} \right)v$

i.e., v²dv = $\frac{P}{M}vdt = \frac{P}{M}dS$

Integrating $\int_{u}^{v}{v^{2}dv} = \frac{P}{M}\int_{0}^{S}{dS}$

v³ – u³ = $\frac{3PS}{M}$

or v =$\left\lbrack \frac{3PS}{M} + u^{3} \right\rbrack^{1/3}$