Car A is traveling at twice the speed of car B. They both hit the brakes at the same time and decrease their velocities at the same rate. If

Question

Car A is traveling at twice the speed of car B. They both hit the brakes at the same time and decrease their velocities at the same rate. If car B travels a distance D before stopping, how far does car A travel before stopping?
A) 4D
B) 2D
C) D
D) D/2
E) D/4

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Hải Đăng 3 years 2021-08-31T18:50:01+00:00 1 Answers 136 views 0

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    0
    2021-08-31T18:51:05+00:00

    Answer:

    A) 4D

    Explanation:

    The distance traveled by the cars before coming to rest can be determined by 3rd equation of motion:

    2as = Vf² – Vi²

    s = (Vf² – Vi²)/2a

    where,

    s = distance traveled

    Vf = Final Speed = 0 m/s

    Vi = Initial Speed

    a = deceleration rate

    First, we consider Car B and we assign a subscript 2 for it:

    Vf₂ = 0 m/s  (As, car finally stops)

    s₂ = D

    a₂ = – a  (due to deceleration)

    D = (0² – Vi₂²) /(-2a)

    D = Vi₂²/2a    ——– equation (1)

    Now, we consider Car A and we assign a subscript 1 for it:

    Vf₁ = 0 m/s  (As, car finally stops)

    s₁ = ?

    a₁ = – a  (due to deceleration)

    Vi₁ = 2 Vi₂  (Since, car A was initially traveling at twice speed of car B)

    s₁ = (0² – Vi₁²) /(-2a)

    s₁ = (2Vi₂)²/2a

    s₁ = 4 (Vi₂²/2a)

    using equation (1), we get:

    s₁ = 4D

    Therefore, the correct option is:

    A) 4D

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