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19 March, 23:58

A model engine accelerated forward from rest along a straight track at 10.0 m/s2 for 3.0 seconds. It then accelerates coward at 16 m/s2 for 5.0 seconds, and finally decelerates at 12 m/s2 until it stops. Calculate how many seconds was the engine moving?

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  1. 20 March, 02:23
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    17.2 seconds

    Explanation:

    Given:

    v₀ = 0 m/s

    a₁ = 10.0 m/s²

    t₁ = 3.0 s

    a₂ = 16 m/s²

    t₂ = 5.0 s

    a₃ = - 12 m/s²

    v₃ = 0 m/s

    Find: t

    First, find v₁:

    v₁ = a₁t₁ + v₀

    v₁ = (10.0 m/s²) (3.0 s) + (0 m/s)

    v₁ = 30 m/s

    Next, find v₂:

    v₂ = a₂t₂ + v₁

    v₂ = (16 m/s²) (5.0 s) + (30 m/s)

    v₂ = 110 m/s

    Finally, find t₃:

    v₃ = a₃t₃ + v₂

    (0 m/s) = (-12 m/s²) t₃ + (110 m/s)

    t₃ = 9.2 s

    The total time is:

    t = t₁ + t₂ + t₃

    t = 3.0 s + 5.0 s + 9.2 s

    t = 17.2 s

    Round as needed.
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