Suppose a car is traveling at 22.8 m/s, and the driver sees a traffic light turn red. After 0.404 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 9.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?

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

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