Answer: The yellow light should last at least 3 seconds.
Step-by-step explanation:
Answer: The yellow light should last at least 3 seconds.
Explanation: To ensure that drivers can stop safely after seeing and responding to the yellow light, we need to calculate the minimum time it takes for a car traveling at the speed limit of 15.0 m/s to come to a stop with a maximum deceleration of -5.0 m/s^2. We can use the following equation of motion:
\[v_f = v_i + at\]
Where:
- \(v_f\) is the final velocity (0 m/s, as the car needs to come to a stop).
- \(v_i\) is the initial velocity (15.0 m/s, the speed limit).
- \(a\) is the deceleration (-5.0 m/s^2, negative because it's deceleration).
- \(t\) is the time we want to find.
Rearranging the equation:
\[0 = 15.0 m/s - 5.0 m/s^2 \cdot t\]
Now, solve for \(t\):
\[t = \frac{15.0 m/s}{5.0 m/s^2} = 3.0 s\]
So, it would take 3 seconds for a car to come to a stop with a maximum deceleration of -5.0 m/s^2. To ensure that drivers have enough time to stop safely after seeing the yellow light, the yellow light should last at least 3 seconds.