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 ≤ 3
(a) Find the velocity at time t.
(b) Find the distance traveled during the given time interval.
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1 answer

if a(t) = 2t + 2
v(t) = t^2 + 2t + c
but v(0) = 3
3 = 0 + 0 + c, c = 3
v(t) = t^2 + 2t + 3
s(t) = (1/3)t^3 + t^2 + 3t + k
s(0) = k
s(3) = 9 + 9 + 9 + k =27+k
distance travelled during the first 3 seconds = 27+k  k = 27 metres 👍
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answered by Reiny
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