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12 December, 14:08

At time t = 0, a 2150-kg rocket in outer space fires an engine that exerts an increasing force on it in the + x-direction. This force obeys the equation F = At^2, where t is time,

and has a magnitude of 781.25 N when r = 1.25 s. (a) Find the SI value of the constant A, including its units. (b) What impulse does the engine exert on the rocket during the I. 50-s

interval starting 2.00 s after the engine is fired? (c) By how much does the rocket? s velocity change during this interval?

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  1. 12 December, 14:25
    0
    a) A = 500 N/s²

    b) I = 5812.50 N-s

    c) Δv = 2.7034 m/s

    Explanation:

    Given info

    m = 2150 kg

    F (t) = At²

    F (1.25 s) = 781.25 N

    a) A = ?

    We use the equation

    F (t) = At² ⇒ 781.25 N = A * (1.25 s) ²

    ⇒ A = F (t) / t² = (781.25 N) / (1.25 s) ²

    ⇒ A = 500 N/s²

    b) I = ? if 2.00 s ≤ t ≤ 3.50 s

    we apply the equation

    I = ∫F (t) dt = ∫At² dt = A ∫t² dt = (500/3) * t³ + C

    Since the limits of integration are 2 and 3.5, we obtain

    I = (500/3) * ((3.5) ³ - (2) ³) = 5812.50 N-s

    c) Δv = ?

    we can apply the equation

    I = m*Δv ⇒ Δv = I / m

    ⇒ Δv = 5812.50 N-s / 2150 kg

    ⇒ Δv = 2.7034 m/s
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