A car is running at the speed of 45km/hr see a child 25 meter ahead and suddenly apllies a brakes. If the retradation of the car is 2 meter

Question

A car is running at the speed of 45km/hr see a child 25 meter ahead and suddenly apllies a brakes. If the retradation of the car is 2 meter per second square,is the child spared?

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Khải Quang 4 years 2021-08-18T00:24:09+00:00 1 Answers 16 views 0

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  1. kiet
    0
    2021-08-18T00:26:01+00:00
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    Answer:

    The car stops in 7.78s and does not spare the child.

    Explanation:

    In order to know if the car stops before the distance to the child, you take into account the following equation:

    x=x_o+v_ot-\frac{1}{2}at^2        (1)

    vo: initial speed of the car = 45km/h

    a: deceleration of the car = 2 m/s^2

    t: time

    xo: initial distance to the child = 25m

    x: final distance to the child = 0m

    It is necessary that the solution of the equation (1) for time t are real.

    You first convert the initial speed to m/s, then replace the values of the parameters and solve the quadratic polynomial for t:

    45\frac{km}{h}*\frac{1h}{3600s}*\frac{1000m}{1km}=12.5\frac{m}{s}

    0=25+12.5t-2t^2\\\\2t^2-12.5t-25=0\\\\t_{1,2}=\frac{-(-12.5)\pm \sqrt{(-12.5)^2-4(2)(-25)}}{2(2)}\\\\t_{1,2}=\frac{12.25\pm 18.87}{4}\\\\t_1=7.78s\\\\t_2=-1.65s

    You take the first value t1 because it has physical meaning.

    The solution for t is real, then, the car stops in 7.78s and does not spare the child.

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