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28 August, 17:33

Calculate the power required to accelerate a 1150 kg car from rest to a final velocity of 30 m/s up a 100 m long uphill road with a slope of 30 degrees from horizontal over a time of 12 seconds. Disregard friction, air drag, and rolling resistance.

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  1. 28 August, 17:38
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    power required is 90.131 kW

    Explanation:

    Given data

    mass of car (m) = 1150 kg

    starting velocity (v1) = 0 m/s

    final velocity (v2) = 30 m/s

    slope angle = 30 degrees

    slope distance = 100 m

    to find out

    power required

    solution

    we know the power = work / time

    here time is given we have calculate the work

    work is for car climb 100 m distance is total sum of potential energy + kinetic energy

    and we know car climb 100m at 30 degree slope so vertical distance (h) will be h = 100 sin (30) = 50 m

    so now potential energy = mass * gravity * height

    potential energy = 1150 * 9.81 * 50 = 564075 J

    kinetic energy = 1/2 * mass * velocity²

    kinetic energy = 1/2 * 1150 * (v2 - v1) ²

    kinetic energy = 1/2 * 1150 * (30 - 0) ² = 517500 J

    now put all value in power formula

    power = work / time

    power = potential energy + kinetic energy / 12

    power = 564075 + 517500 / 12 = 90131.25 W

    power = 90.131 kW
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