$\mathbf{a})$

$v\left(t\right)=s^{\prime }\left(t\right)$

$v\left(t\right)={\left(1-2t+3t^2-0,5t^3\right)}^{\prime }=$

$={\left(1\right)}^{\prime }-{\left(2t\right)}^{\prime }+{\left(3t^2\right)}^{\prime }-{\left(0,5t^3\right)}^{\prime }=$

$=0-2{\left(t\right)}^{\prime }+3{\left(t^2\right)}^{\prime }-0,5{\left(t^3\right)}^{\prime }=$

$=-2+3\cdot 2t-0,5\cdot 3t^2=$

$=-2+6t-1,5t^2$

$a\left(t\right)=v^{\prime }\left(t\right)$

$a\left(t\right)={\left(-2+16t-1,5t^2\right)}^{\prime }=$

$={\left(-2\right)}^{\prime }+{\left(16t\right)}^{\prime }-{\left(1,5t^2\right)}^{\prime }=$

$=0+16{\left(t\right)}^{\prime }-1,5{\left(t^2\right)}^{\prime }=$

$=16-1,5\cdot 2t=$

$=16-3t$