I've been working on the following problems, and I know how to integrate functions,but I do not know how to find the value of "c" in the examples below when finding the antiderivative. Any idea what to do? Cheers
A particle travels in a straight line such that its acceleration at time t seconds is equal to $6t+1$ $m/s^2$. When $t=2$, the displacement is equals to $ 12m$ and when $t=3 $ the displacement is equals to $ 34m$. Find the displacement and velocity when $t=4$.
A particle travels in a straight line with its acceleration at time t equal to $3t+2$ $ m/s^2$. The particle has an initial positive velocity and travels $30m$ in the fourth second. Find the velocity of the body when $t=5$.