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9 June, 18:36

The engine of a locomotive exerts a constant force of 8.0 105 N to accelerate a train to 82 km/h. Determine the time (in min) taken for the train of mass 1.7 107 kg to reach this speed from rest. min

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  1. 9 June, 18:58
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    It will take the train 8.2 min to reach a speed of 82 km/h

    Explanation:

    Hi there!

    Using Newton's second law, we can calculate the acceleration of the train:

    F = m · a

    Where:

    F = force exerted by the locomotive.

    m = mass of the train.

    a = acceleration of the train.

    Solving the equation for the acceleration:

    F/m = a

    8.0 * 10⁵ N / 1.7 * 10⁷ kg = a

    a = 4.7 * 10⁻² m/s²

    Let's convert 82 km/h to m/s:

    82 km/h · (1000 m / 1 km) · (1 h / 3600 s) = 23 m/s

    Using the equation of velocity, we can calculate the time it takes for the train to reach a velocity of 23 m/s.

    v = v0 + a · t

    Where:

    v = velocity at time "t".

    v0 = initial velocity (in this case, v0 = 0 because the train starts from rest).

    a = acceleration.

    t = time.

    23 m/s = 0 + 4.7 * 10⁻² m/s² · t

    t = 23 m/s / 4.7 * 10⁻² m/s²

    t = 4.9 * 10² s

    Let's convert the seconds into minutes:

    4.9 * 10² s · (1 min / 60 s) = 8.2 min

    It will take the train 8.2 min to reach a speed of 82 km/h
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