When a high-speed passenger train traveling at 161 km/h rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance D=676 m ahead (figure). The locomotive is moving at 29.0 km/h. The engineer of the high-speed train immediately applies the brakes. What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided?
Let us denote v_t to be the initial velocity of the train and v_l to be the locomotive’s velocity. Note that v_l is also the final velocity of the train if the collision is barely avoided. We will also denote \triangle x to be the distance between two trains and the distance the train travels forward during this time by the locomotive. Thus, we can write:
We can now use v=v_0+at to eliminate t from the equation. Thus, we can write:
Isolating for a gives us:
Substituting the values given in the question gives us:
Let us now convert this to m/s^2.
Thus, the magnitude of the acceleration is \mid a\mid=0.944m/s^2
This question can be found in Fundamentals of Physics, 10th edition, chapter 2, question 43.