Little Room to Brake

Overview

The train approaches a platform via a bridge from a distance $\Delta x$ with an initial velocity of $v_{0x}$.

Calculate and set the correct braking acceleration (deceleration) $a_x$ so the train stops completely on the platform.

If the deceleration is too high, the train stops early on the bridge, causing it to collapse. If the deceleration is too low, the train overshoots the platform and falls off the cliff.

Relevant Equations

$$ v_x = v_{x0} + a_x t $$ $$ x = x_0 + v_{x0} t + \frac{1}{2}a_x t^2 $$ $$ v_x^2 = v_{x0}^2 + 2a_x(x - x_0) $$