Explanation

(b) $a = \frac{dv}{dt} = 6t + 5$ or $dv = (6t + 5)dt$
Integrating it, we have
$v = \frac{6t^{2}}{2} + 5t + C = 3t^{2} + 5t + C$
where $C$ is constant of integration
When $v = 0$ so $c = 0$
$\therefore v = \frac{ds}{dt} = 3t^{2} + 5t$ or $ds = (3t^{2} + 5t)dt$
Integrating it within the conditions of motion $ie,$ as $t$ changes from 0 to 1 s changes from 0 to s, we have $s = t^{3} + \frac{5t^{2}}{2} = 1 + \frac{5}{2} = 3.5$m.