A particle $is$ moving with acceleration $a(t)=24t+12\frac{m}{s^2}$

velocity $at$ time $t=0isv(0)=15\frac{m}{s}$

position $at$ time $t=0iss(0)=4m$

First, $$ find the general solution for the velocity function, with unknown constant $of$ integration:

$v_{\text{g}\text{e}\text{n}}=$

Next, $or$ use the given known$-$velocity $at$ a known$-$time $to$ find the particular velocity function.

$v(t)=\frac{m}{s}$

Now $do$ the same steps, integrating and finding the constant $of$ integration, $to$ find the general

and particular position functions.

$s_{\text{g}\text{e}\text{n}}(t)=$

$s(t)=m$

$We$ can predict the future now! What will $be$ the particle's position when $t=7?$

$s(7)=,m$