The correct answer is $\boxed{\text{C}}$.
The Mean Value Theorem states that if a function $f$ is continuous on the interval $[a, b]$, then there exists a point $c$ in $(a, b)$ such that $f'(c) = \frac{f(b) – f(a)}{b – a}$.
In this case, the function $f$ is the speed of the train, and the interval is $[0, 8]$. We know that $f(0) = 0$ and $f(8) = 280$. Therefore, by the Mean Value Theorem, there exists a point $c$ in $(0, 8)$ such that $f'(c) = \frac{280 – 0}{8} = 35$.
The speedometer measures the instantaneous speed of the train, so the speedometer must read exactly 35 kmph at some point during the acceleration.
Option A is incorrect because the train is not moving at 0 kmph at any point during the acceleration.
Option B is incorrect because the train is moving at a speed greater than 8 kmph at some point during the acceleration.
Option D is incorrect because the train is not moving at a speed of 126 kmph at any point during the acceleration.