You are following 25 m behind another car on the highway while talking on the cell phone. Both you and the other car initially

You are following 25 m behind another car on the highway while talking on the cell phone. Both you and the other car initially have a constant speed of 110 km/hr. You being to argue with the person on the phone and become distracted from the road for 2 seconds. At the beginning of that two seconds, the other car sees something in the road ahead and begins to break hard, at 5 m/s^2 . Required:
a. How far apart are the two cars when your attention returns to the road?
b. After you look back at the road (after the 2 seconds of interruption), you take another 0.4 seconds to realize the danger and begin braking, also at 5 m/s? Will you be able to stop in time?
c. If yes, what is the distance between the cars when they are both at rest? If no, what is your speed when you strike the other car?

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  1. Δx = 10 m

    Explanation:

    For this problem we can calculate the distance traveled by each car in the time of 2 s

    let's reduce the speed to the SI system

    v = 110 km / h (1000m / 1 km) (1 h / 3600 s) = 30.556 m / s

         

    Cart 1

    this car has constant speed

                v = x₁ / t

                x₁ = v t

                x₁ = 30,556  2

                x₁ = 61.11 m

    This car is that of the person with the cell phone

    Cart 2

    this car has an acceleration of a = 5 m / s²

                x₂ = v₀ t - ½ a t²

                x₂ = 30,556 2 - ½ 5 2²

                x₂ = 51,112 m

    The difference in distance between the two vehicles is

                Δx = x₁ - x₂

                Δx = 61.11 - 51.11

                Δx = 10 m

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