The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0

Question

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 4 (a) Find the velocity at time t. v(t) = m/s (b) Find the distance traveled during the given time interval. m

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Khánh Gia 4 years 2021-08-22T17:55:17+00:00 1 Answers 363 views 0

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  1. Tryphena
    0
    2021-08-22T17:57:15+00:00
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    Answer:

    V(t) = 2t^2 + 2t - 3

    \Delta S = 46.667\ m

    Explanation:

    We can find the velocity at time t using the formula:

    V(t) = V(0) + a*t

    Where V(t) is the velocity at time t, V(0) is the inicial velocity and a is the acceleration.

    Then we have that:

    V(t) = -3 + (2t+2)*t

    V(t) = 2t^2 + 2t - 3

    If we integrate the velocity in the time, we find the displacement (distance traveled):

    \int {V(t)} \, dt = 2t^3/3 + t^2 - 3t + c

    \Delta S = \int\limits^4_0 {V(t)} \, dt = (2*4^3/3 + 4^2 - 3*4) - (2*0^3/3 + 0^2 - 3*0)

    \Delta S = 46.667\ m

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )