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 330 m from the crossing
and its speed is 21 m/s.
If the engineer’s reaction time is 0.44 s,
what should be the magnitude of the minimum deceleration to avoid an accident?
Answer in units of m/s
2
.
To find the magnitude of the minimum deceleration needed to avoid an accident, we need to calculate the stopping distance of the train during the engineer's reaction time.
1. Calculate the distance traveled by the train during the engineer's reaction time:
Distance = Speed * Time
Distance = 21 m/s * 0.44 s
Distance = 9.24 m
2. Subtract the distance traveled during the reaction time from the initial distance of the train from the crossing:
Distance remaining = Initial distance - Distance during reaction time
Distance remaining = 330 m - 9.24 m
Distance remaining = 320.76 m
3. To avoid an accident, the train should come to a stop before reaching the car. Therefore, the stopping distance should be equal to or less than the remaining distance.
4. Use the formula for stopping distance:
Stopping distance = (Initial velocity^2) / (2 * acceleration)
Consider the velocity of the train when it starts decelerating to be 0, as it needs to come to a stop.
So, the stopping distance is:
320.76 m = (0^2) / (2 * acceleration)
5. Rearrange the equation to solve for acceleration:
acceleration = (0^2) / (2 * stopping distance)
acceleration = 0 / (2 * 320.76 m)
acceleration = 0 m/s^2
Therefore, the magnitude of the minimum deceleration needed to avoid an accident is 0 m/s^2. In this case, the train cannot come to a stop before reaching the car within the given reaction time.