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25 May, 04:48

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 49 m in front of you. You reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10m/s2.

a. How much distance is between you and the deer when you come to a stop?

b. What is the maximum speed you could have and still not hit the deer?

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  1. 25 May, 05:05
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    v = 26.7 m/s

    Explanation:

    Given,

    speed of the car = 20 m/s

    distance between the car and the deer = 49 m

    time taken to press the brake = 0.50 s

    maximum deceleration of the car = 10 m/s²

    Now,

    distance travel by the car in 0.5 s = u x t = 20 x 0.5 = 10 m

    distance travel by the car after the break is pressed

    Using equation of motion

    v² = u² + 2 a s

    0² = 20² - 2 x 10 x s

    s = 20 m

    Total distance travel by the car = 20 + 10 = 30 m

    Distance between deer and car = 49-30 = 19 m.

    b. Maximum speed a car could have

    Distance travel by the car in reaction time = v' x 0.5

    v' is the maximum speed of the car.

    maximum distance car can cover = 49 - 0.5 v'

    Now, Using equation of motion

    v² = u² + 2 a s

    0² = v'² - 2 x 10 x (49 - 0.5 x v')

    v'² + 10 v' - 980 = 0

    By solving

    v = 26.7 m/s

    Hence, maximum speed of the car can be 26.7 m/s
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