he acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.

Question

a(t) = 2t + 2,    v(0) = −3,    0 ≤ t ≤ 5

(a) Find the velocity at time t.

(b) Find the distance traveled during the given time interval.

Answer 1

a = 2t + 2 = v'

v(0)=-3

v(t) = integral of a(t) = t^2 +2t + c

v(0) = -3 = c

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

s(t) = integral of v(t) = t^3/3 +t^2 -3t + c2

s(5) - s(0) = 125/3 + 25 -15 = 155/3 = 51 2/3 meters in 5 seconds