Question

Find the total distance traveled during the first 8s for v = 3t^2 - 24t + 36 -- just tell me what steps i'm supposed to follow to to this, i know the particle is at rest at t = 2,6 and moving in the positive direction when 0=6

Answer 1

Velocity is the derivative of distance, so integrate:
\[v = 3t ^{2} - 24t + 36\]
And input 8 for t.

Answer 2

find
\[\int\limits_{0}^{8} (3t^2 - 24t + 36) dt\]