Final answer:
To calculate the train's acceleration, we use the kinematic equation, resulting in an acceleration of – 8 m/s², which is a deceleration.
Step-by-step explanation:
The question asks us to calculate the acceleration of a train as it brakes from 40 m/s to a stop over a distance of 100 m. The formula to find acceleration when we know the initial velocity (v0), final velocity (v), and distance (s) is derived from the kinematic equation v2 = v02 + 2as, where 'a' is the acceleration. As the train comes to a stop, the final velocity v = 0 m/s. Rearranging the equation to solve for 'a' gives us a = (v2 - v02)/(2s).
Substituting the known values we get a = (0 - (40 m/s)2)/(2 × 100 m) = -1600 m2/s2/200 m = -8 m/s2. The negative sign indicates that this is a deceleration, as expected when a train comes to a stop.