The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) = t + 8,v(0) = 5,0 ≤ t ≤ 10,Find the distance traveled during the given time interval

Answer 1

Well to find v(t) integrate a(t)

v(t) = 0.5 t² + 8t + c

v(0) = 5 giving c = -52.5

v(t) = 0.5 t² + 8t - 52.5

To find s(t) integrate v(t)

s(t) = (0.5/3) t³ + 4t² - 52.5t + C

Presumably s(0) = 0 although it isn't given, so C = 0

Now find s(10)