A car accelerates from rest of $$u$$ m s$$^{-1}$$. The energy spent in this process is $$E$$ J. The energy required to accelerate the car from $$u$$ m s$$^{-1}$$ to $$2u$$ m s$$^{-1}$$ is $$nE$$ J. The value of $$n$$ is _____.

Energy spent to accelerate from rest to $$u$$ m/s:

$$E = \frac{1}{2}mu^2$$

Energy spent to accelerate from $$u$$ to $$2u$$ m/s:

$$E' = \frac{1}{2}m(2u)^2 - \frac{1}{2}mu^2 = \frac{1}{2}m(4u^2 - u^2) = \frac{3}{2}mu^2 = 3E$$

Therefore $$n = 3$$.

This matches the answer key value of $$\mathbf{3}$$.