You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fas

Question

You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under identical conditions?

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Neala 5 years 2021-08-28T14:04:52+00:00 1 Answers 63 views 0

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  1. yenoanh
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    2021-08-28T14:06:24+00:00
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    Answer:

    So the car would skid 4 times the initial skidding displacement under the identical conditions when the car’s initial velocity is just double.

    Explanation:

    Under identical conditions when the brakes are applied for the same body moving with twice the initial speed then we can analyse using the equation of motion.

    Initially:

    v^2=u^2-2a.s

    \Rightarrow s=\frac{u^2}{2a} ………………………(1)

    where:

    v= final velocity of the car = 0 (because the car stops)

    u= initial velocity of the car

    a= acceleration of the car (here it is deceleration and hence taken with negative sign)

    s= displacement of the car before stopping

    Final condition:

    Initial velocity is, 2u

    So,

    v^2=(2u)^2-2a.s'

    0^2=4u^2-2a.s'

    s'=\frac{4u^2}{2a}

    s'=\frac{2u^2}{a} ………………………..(2)

    Now divide eq. (2) by (1)

    \frac{s'}{s}=4

    So the car would skid 4 times the initial skidding displacement under the identical conditions when the car’s initial velocity is just double.

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