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 ≤ 5
(a) Find the velocity at time t.
v(t) = ______ m/s
(b) Find the distance traveled during the given time interval.
_____ m

Thank you!

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  1. v(t) = ∫a(t) dt = ∫(2t+2) dt = t^2+2t+C
    v(0) = -3, so C = -3
    v(t) = t^2+2t-3

    s(t) = ∫[0,5] v(t) dt = ...

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  2. The first part was correct and I got 155/3 m for B however, my homework system won't take that answer and doesn't want it as a decimal either. That is the answer, correct?

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  3. NO - I did this last night

    The thing moves backwards from zero
    then forward again

    You found the displacement, not the distance.

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  5. That was my bad, but he should have read and analyzed your solution.

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