Kevin S. Huang

2008: Problem 19

Topic: Energy
Concepts: Kinetic energy, Power

Solution:

Since there is no energy loss, all power from the engine goes to kinetic energy,

E=Pt=\frac{1}{2}mv^2

v=\sqrt{\frac{2Pt}{m}}

The instantaneous power is given by

P=Fv=mav

Substituting our expression for the velocity,

P=ma\sqrt{\frac{2Pt}{m}}

a \propto \frac{1}{\sqrt{t}}

If the time is doubled, the acceleration decreases by a factor of $\sqrt{2}$ ,

a=\frac{a_0}{\sqrt{2}}

so the answer is B.