Answer:
38.09 m
Explanation:
We'll begin by calculating the distance travelled by the car during the reaction time. This can be obtained as follow:
Reaction time (tᵣ) = 0.404 s
Initial velocity (u) = 22.8 m/s,
Distance travelled during the reaction time (sᵣ) =?
sᵣ = utᵣ
sᵣ = 22.8 × 0.404
sᵣ = 9.21 m
Next, we shall determine the distance travelled by the car when the brake was applied. This can be obtained as follow:
Initial velocity (u) = 22.8 m/s
Acceleration (a) = –9 m/s² (since the car is decelerating)
Final velocity (v) = 0 m/s
Distance travelled when the brake was applied (s₆) =?
v² = u² + 2as₆
0² = 22.8² + (2 × –9 × s₆)
0 = 519.84 – 18s₆
Collect like terms
0 – 519.84 = –18s₆
–519.84 = –18s₆
Divide both side by –18
s₆ = –519.84 / –18
s₆ = 28.88 m
Finally, we shall determine the stopping distance of the car, as measured from the point where the driver first notices the red light. This can be obtained as follow:
Distance travelled during the reaction time (sᵣ) = 9.21 m
Distance travelled when the brake was applied (s₆) = 28.88 m
Stopping distance =?
Stopping distance = sᵣ + s₆
Stopping distance = 9.21 + 28.88
Stopping distance = 38.09 m
