An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 8.71 m from the crossing and its speed is 8.44 m/s. If the engineer’s reaction time is 9.34 s, what should be the magnitude of the minimum deceleration to avoid an accident? Answer in units of m/s/s

Question

An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 8.71 m from the crossing and its speed is 8.44 m/s. If the engineer’s reaction time is 9.34 s, what should be the magnitude of the minimum deceleration to avoid an accident? Answer in units of m/s/s

Answer 1

To find the minimum deceleration required to avoid an accident, we need to determine the time it takes for the train to come to a stop from the moment the engineer sees the car. We can then calculate the deceleration using the formula:

acceleration = (final velocity - initial velocity) / time

First, let's find the time it takes for the train to stop. This is equal to the reaction time plus the time it takes for the train to travel a distance of 8.71 m at a speed of 8.44 m/s:

total time = reaction time + distance / speed
= 9.34 s + 8.71 m / 8.44 m/s

Now, let's calculate the acceleration using the formula:

acceleration = (0 m/s - 8.44 m/s) / total time

Substituting the values:

acceleration = (-8.44 m/s) / (9.34 s + 8.71 m / 8.44 m/s)

Simplifying the expression:

acceleration = (-8.44 m/s) / (9.34 s + 1.03 s)
= (-8.44 m/s) / (10.37 s)

Finally, calculating the value:

acceleration ≈ -0.813 m/s^2

Therefore, the magnitude of the minimum deceleration required to avoid an accident is approximately 0.813 m/s^2. Note that the negative sign indicates that the train is decelerating or slowing down.