Answer
$s(t)=16t^2-2t+1$
Work Step by Step
Since, the derivative of the function$s=\dfrac{ds}{dt}=32t-2$ is $s(t)=16t^2-2t+C$
As we are given that $s(0.5)=4$
This implies that $s(0.5)=4$
or, $4=16(0.5)^2-2(0.5)+C \implies C=1$
Hence, $s(t)=16t^2-2t+1$